Electromagnetic frequency converter

Abstract

An electromagnetic frequency converter includes an atomic ensemble; one or more first sources (6, 8) of electromagnetic radiation (P, R) to be incident upon the atomic ensemble to excite atomic valence electrons from a ground state to a first Rydberg state; one or more second sources (6, 14) of electromagnetic radiation (A, C) to be incident upon the atomic ensemble to excite atomic valence electrons from an excited state to a second Rydberg state; a first input (20) and/or output (26) for electromagnetic radiation (L) to be incident upon the atomic ensemble from the first input or received from the atomic ensemble at the first output; and a second input (14) and/or output (24) for electromagnetic radiation (M) to be incident upon the atomic ensemble from the second input or received from the atomic ensemble at the second output.

Claims

1. An electromagnetic frequency converter for converting input electromagnetic radiation to output electromagnetic radiation of a different frequency, the electromagnetic frequency converter comprising: an atomic ensemble; one or more first sources of electromagnetic radiation each having a frequency selected from a set of possible atomic transition frequencies for the atomic valence electrons in the atomic ensemble, wherein the sum of the frequencies of the one or more first sources is between 600 THz and 1500 THz, wherein the electromagnetic radiation from the one or more first sources is arranged to be incident upon the atomic ensemble to excite atomic valence electrons in the atomic ensemble from a ground state to a first Rydberg state; one or more second sources of electromagnetic radiation each having a frequency selected from a set of possible atomic transition frequencies for the atomic valence electrons in the atomic ensemble, wherein the sum of the frequencies of the one or more second sources is between 300 THz and 750 THz, wherein the electromagnetic radiation from the one or more second sources is arranged to be incident upon the atomic ensemble to excite atomic valence electrons in the atomic ensemble from an excited state to a second Rydberg state, wherein the excited state is linked to the ground state by an atomic transition having a frequency between 193 THz and 800 THz for the atomic valence electrons in the atomic ensemble, and the second Rydberg state is linked to the first Rydberg state by an atomic transition having a frequency between 300 MHz and 3 THz for the atomic valence electrons in the atomic ensemble; a first input and/or output for electromagnetic radiation having a frequency between 193 THz and 800 THz, wherein the first input or output is arranged to be coupled to the atomic ensemble such that the electromagnetic radiation is incident upon the atomic ensemble from the first input or received from the atomic ensemble at the first output; and a second input and/or output for electromagnetic radiation having a frequency between frequency between 300 MHz and 3 THz, wherein the second input or output is arranged to be coupled to the atomic ensemble such that the electromagnetic radiation is incident upon the atomic ensemble from the second input or received from the atomic ensemble at the second output; wherein the electromagnetic frequency converter is arranged such that on application of the one or more first and one or more second sources of electromagnetic radiation to be incident upon the atomic ensemble, input of electromagnetic radiation having a frequency between 193 THz and 800 THz from the first input and which couples to the atomic transition between the ground state and the excited state or input of electromagnetic radiation having a frequency between 300 MHz and 3 THz from the second input and which couples to the atomic transition between the first Rydberg state and the second Rydberg state, causes electromagnetic radiation having a frequency between 300 MHz and 3 THz from the atomic transition between the second Rydberg state and the first Rydberg state to be output from the second output or electromagnetic radiation having a frequency between 193 THz and 800 THz from the atomic transition between the excited state and the ground state to be output from the first output respectively.

2. The electromagnetic frequency converter of claim 1, wherein the one or more first sources of electromagnetic radiation comprise: one or more first sources of electromagnetic radiation each having a frequency selected from a set of possible atomic transition frequencies for the atomic valence electrons in the atomic ensemble, wherein the sum of the frequencies of the one or more first sources is between 193 THz and 800 THz, wherein the electromagnetic radiation from the one or more first sources is arranged to be incident upon the atomic ensemble to excite atomic valence electrons in the atomic ensemble from a ground state to an intermediate excited state; and one or more third sources of electromagnetic radiation each having a frequency selected from a set of possible atomic transition frequencies for the atomic valence electrons in the atomic ensemble, wherein the sum of the frequencies of the one or more third sources is between 193 THz and 800 THz, wherein the electromagnetic radiation from the one or more third sources is arranged to be incident upon the atomic ensemble to excite atomic valence electrons in the atomic ensemble from the intermediate excited state to the first Rydberg state.

3. The electromagnetic frequency converter of claim 2, wherein the intermediate excited state of the valence electrons in the atomic ensemble that is reached by excitation by the one or more first sources and the excited state of the valence electrons in the atomic ensemble that is reached by excitation by the first input have the same principal quantum number but comprise a different hyperfine state.

4. The electromagnetic frequency converter of claim 2, wherein when the electromagnetic frequency converter comprises a first source, a second source, a third source and a fourth source, the frequencies and intensities of the electromagnetic radiation from the first, second, third and fourth sources satisfy the following conditions: ${}_5=\frac{{.Math.{}_4.Math.}^2}{{}_4};{}_6=\frac{{.Math.{}_{2a}.Math.}^2}{{}_5};\mathrm{and}.Math.{}_3.Math..Math.{}_1.Math.,$ where .sub.1 is the Rabi frequency of the electromagnetic radiation from the first source, .sub.2 is the Rabi frequency of the electromagnetic radiation from the second source, .sub.3 is the Rabi frequency of the electromagnetic radiation from the third source, .sub.4 is the Rabi frequency of the electromagnetic radiation from the fourth source, .sub.4-.sub.5 is the detuning of the electromagnetic radiation from the fourth source from the atomic transition between the third Rydberg state and the second Rydberg state, and .sub.5-.sub.6 is the detuning of the electromagnetic radiation from the second source from the atomic transition between the third Rydberg state and the excited state.

5. The electromagnetic frequency converter of claim 1, wherein the one or more second sources of electromagnetic radiation comprise: one or more second sources of electromagnetic radiation each having a frequency selected from a set of possible atomic transition frequencies for the atomic valence electrons in the atomic ensemble, wherein the sum of the frequencies of the one or more second sources is between 300 THz and 750 THz, wherein the electromagnetic radiation from the one or more second sources is arranged to be incident upon the atomic ensemble to excite atomic valence electrons in the atomic ensemble from an excited state to a third Rydberg state; and one or more fourth sources of electromagnetic radiation each having a frequency selected from a set of possible atomic transition frequencies for the atomic valence electrons in the atomic ensemble, wherein the sum of the frequencies of the one or more fourth sources is between 300 MHz and 3 THz, wherein the electromagnetic radiation from the one or more fourth sources is arranged to be incident upon the atomic ensemble to excite atomic valence electrons in the atomic ensemble from the third Rydberg state to the second Rydberg state.

6. The electromagnetic frequency converter of claim 5, wherein the one or more fourth sources comprises a microwave or terahertz radiation generator and a waveguide arranged to couple the microwave or terahertz radiation generated by the microwave or terahertz radiation generator to the atomic ensemble so that the microwave or terahertz radiation is incident upon the atomic ensemble.

7. The electromagnetic frequency converter of claim 1, wherein the atomic ensemble comprises alkali metal atoms.

8. The electromagnetic frequency converter of claim 1, wherein the atomic ensemble comprises rubidium atoms, caesium atoms or sodium atoms.

9. The electromagnetic frequency converter of claim 1, further comprising a vapour cell within which the atomic ensemble is held.

10. The electromagnetic frequency converter of claim 9, wherein the vapour cell comprises an input window transparent to the electromagnetic radiation from one or more of: the one or more first sources of electromagnetic radiation, the one or more second sources of electromagnetic radiation, the first input for electromagnetic radiation and the second input for electromagnetic radiation, which are arranged to direct the respective electromagnetic radiation therefrom through the input window so to be incident upon the atomic ensemble.

11. The electromagnetic frequency converter of claim 9, wherein the vapour cell comprises an output window transparent to the electromagnetic radiation from one or both of the first output for electromagnetic radiation and the second output for electromagnetic radiation, where are arranged to receive the electromagnetic radiation from the atomic ensemble through the output window.

12. The electromagnetic frequency converter of claim 9, wherein the electromagnetic frequency converter comprises a heater in good thermal communication with the vapour cell and arranged to heat the atomic ensemble.

13. The electromagnetic frequency converter of claim 1, wherein one or more of the one or more first sources and the one or more second sources of electromagnetic radiation comprises a laser.

14. The electromagnetic frequency converter of claim 1, wherein the second output comprises a waveguide arranged to collect the electromagnetic radiation having a frequency between 0.1 mm and 1 m output from the atomic ensemble.

15. The electromagnetic frequency converter of claim 1, wherein one or more of the transitions of the atomic valence electrons are electric dipole transitions.

16. The electromagnetic frequency converter of claim 1, wherein the transitions between the ground state and the excited state of the valence electrons in the atomic ensemble are at least one of the D-lines transitions.

17. The electromagnetic frequency converter of claim 1, wherein the first and second Rydberg states have a principal quantum number between 20 and 80.

18. The electromagnetic frequency converter of claim 1, wherein the first Rydberg state and the second Rydberg state have the same principal quantum number but comprise one or more of a different azimuthal quantum number and a different orbital angular momentum quantum number.

19. The electromagnetic frequency converter of claim 1, wherein when the input electromagnetic radiation is input from the second input, the difference in the frequency of the second input electromagnetic radiation and the frequency of the atomic transition between the first and second Rydberg states of the valence electrons of the atomic ensemble is much less than the frequency of the transition between the first and second Rydberg states itself.

20. The electromagnetic frequency converter of claim 1, wherein when the electromagnetic radiation is input from the first input, the difference in the frequency of the first input electromagnetic radiation and the frequency of the atomic transition between the ground and excited state of the valence electrons of the atomic ensemble is much less than the frequency of the transition between the ground and excited states itself.

21. A method of converting input electromagnetic radiation to output electromagnetic radiation of a different frequency, the method comprising: exciting atomic valence electrons in an atomic ensemble from a ground state to a first Rydberg state by arranging for electromagnetic radiation from one or more first sources of electromagnetic radiation to be incident upon the atomic ensemble, wherein the frequency of each of the one or more first sources of electromagnetic radiation is selected from a set of possible atomic transition frequencies for the atomic valence electrons in the atomic ensemble and the sum of the frequencies of the one or more first sources is between 600 THz and 1500 THz; exciting atomic valence electrons in the atomic ensemble from an excited state to a second Rydberg state by arranging for electromagnetic radiation from one or more second sources of electromagnetic radiation to be incident upon the atomic ensemble, wherein the excited state is linked to the ground state by an atomic transition having a frequency between 193 THz and 800 THz for the atomic valence electrons in the atomic ensemble, and the second Rydberg state is linked to the first Rydberg state by an atomic transition having a frequency between 300 MHz and 3 THz for the atomic valence electrons in the atomic ensemble, and wherein the frequency of each of the one or more second sources of electromagnetic radiation is selected from a set of possible atomic transition frequencies for the atomic valence electrons in the atomic ensemble and the sum of the frequencies of the one or more second sources is between 300 THz and 750 THz; inputting electromagnetic radiation having a frequency between 193 THz and 800 THz or between 300 MHz and 3 THz to the atomic ensemble such that the electromagnetic radiation is incident upon the atomic ensemble; wherein the atomic ensemble is arranged such that on application of the one or more first and one or more second sources of electromagnetic radiation to be incident upon the atomic ensemble, input of electromagnetic radiation having a frequency between 193 THz and 800 THz from the first input and which couples to the atomic transition between the ground state and the excited state or input of electromagnetic radiation having a frequency between 300 MHz and 3 THz from the second input and which couples to the transition between the first Rydberg state and the second Rydberg state, causes electromagnetic radiation having a frequency between 300 MHz and 3 THz from the atomic transition between the second Rydberg state and the first Rydberg state or electromagnetic radiation having a frequency between 193 THz and 800 THz from the atomic transition between the excited state and the ground state to be output from the atomic ensemble.

Description

(1) Embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

(2) FIG. 1 is a schematic diagram showing an electromagnetic frequency converter according to an embodiment of the present invention;

(3) FIG. 2 shows an atomic level scheme used in an electromagnetic frequency converter according to an embodiment of the present invention;

(4) FIG. 3 shows an specific example of an atomic level scheme used in an electromagnetic frequency converter according to an embodiment of the present invention;

(5) FIGS. 4a and 4b show simulation plots of the intensities of input electromagnetic radiation frequencies into the embodiment of the electromagnetic frequency converter operated according to the atomic level scheme shown in FIG. 3;

(6) FIG. 5 shows another specific example of an atomic level scheme used in an electromagnetic frequency converter according to an embodiment of the present invention; and

(7) FIGS. 6a and 6b show simulation plots of the intensities of input electromagnetic radiation frequencies into the embodiment of the electromagnetic frequency converter operated according to the atomic level scheme shown in FIG. 3.

(8) A preferred embodiment of the electromagnetic frequency converter will now be described, which allows conversion of an optical or near-infrared frequency input into a microwave or terahertz frequency output, or vice versa. Such a converter has many uses, e.g. in the fields of telecommunications, opto-electronics and quantum computing.

(9) FIG. 1 is a schematic diagram showing an electromagnetic frequency converter 1 according to an embodiment of the present invention. The electromagnetic frequency converter 1 includes a vapour cell 2 containing an atomic ensemble 4, e.g. of rubidium, caesium or sodium atoms. The vapour cell 2 includes a heater (not shown) to vaporise the atoms of the atomic ensemble 4. In one embodiment the vapour cell 2 is a cylinder having a diameter of approximately 1 cm and a length of approximately 2 cm.

(10) The electromagnetic frequency converter 1 also includes first and second lasers 6, 8 that act as sources of optical or near-infrared radiation A, P to be incident upon the atomic ensemble 4 within the vapour cell 2. The vapour cell 2 has a window 10 at one end that is transparent to the frequencies of the optical or near-infrared radiation A, P from the lasers 6, 8, which are arranged to direct their optical or near-infrared radiation A, P into the vapour cell 2 through the window 10, so as to be incident upon the atomic ensemble 4.

(11) Half of the optical or near-infrared radiation A from the first laser 6 is separated from the rest of the laser beam and directed through a frequency shifter 12 to shift the frequency of the optical or near-infrared radiation before the optical or near-infrared radiation with the shifted frequency R is directed through the window 10 of the vapour cell 2 so as to be incident upon the atomic ensemble 4.

(12) The electromagnetic frequency converter 1 further includes a microwave or terahertz radiation generator 14 that acts as a source of microwave or terahertz radiation C to be incident upon the atomic ensemble 4 within the vapour cell 2. The vapour cell 2 has a window 16 at one side, lying perpendicular to the window 10 for the input optical or near-infrared radiation A, R, P, that is transparent to the frequencies of the microwave or terahertz radiation C from the microwave or terahertz radiation generator 14. A waveguide 18 is used to carry the microwave or terahertz radiation C from the microwave or terahertz radiation generator 14 and to direct the microwave or terahertz radiation C into the vapour cell 2 through the window 16, so as to be incident upon the atomic ensemble 4.

(13) The electromagnetic frequency converter 1 further includes an optical or near-infrared radiation input 20 that is arranged to input optical or near-infrared radiation L into the vapour cell 2 through the window 10 transparent to optical or near-infrared radiation, so as to be incident upon the atomic ensemble 4. The electromagnetic frequency converter 1 also includes a microwave or terahertz radiation input 22 that is arranged to input microwave or terahertz radiation M into the vapour cell 2 through the window 16 transparent to microwave or terahertz radiation, so as to be incident upon the atomic ensemble 4.

(14) The electromagnetic frequency converter 1 also includes a microwave or terahertz radiation output 24 and an optical or near-infrared radiation output 26. The microwave or terahertz radiation output 24 is arranged to receive microwave or terahertz radiation that is output from the atomic ensemble 4 in the vapour cell 2 via a window 28 and a waveguide 30. The output window 28 in the vapour cell 2 is transparent to the frequency(s) of the microwave or terahertz radiation that is output from the atomic ensemble 4 within the vapour cell 2, and is arranged on the opposite side of the vapour cell 2 from the input window 16 for microwave or terahertz radiation.

(15) The optical or near-infrared radiation output 26 is arranged to receive optical or near-infrared radiation that is output from the atomic ensemble 4 in the vapour cell 2 via a window 32. The output window 32 in the vapour cell 2 is transparent to the frequency(s) of the optical or near-infrared radiation that is output from the atomic ensemble 4 within the vapour cell 2, and is arranged on the opposite side of the vapour cell 2 from the input window 10 for optical or near-infrared radiation.

(16) The embodiment of the electromagnetic frequency converter 1 shown in FIG. 1 is able to operate in two main modes of operation: to convert microwave or terahertz radiation into optical or near-infrared radiation and vice versa. Both modes of operation will now be described with reference to FIGS. 1 and 2. FIG. 2 is an atomic level scheme used in the electromagnetic frequency converter 1.

(17) In both modes of operation, the atomic ensemble 4 is prepared in the vapour cell 2 and the heater is energised to vaporise the atoms of the atomic ensemble 4. The first and second lasers 6, 8 are energised, with a portion, e.g. half, of the optical or near-infrared radiation from the first laser 6 being separated from the rest of the laser beam and directed through the frequency shifter 12 to shift the frequency of the optical or near-infrared radiation. The optical or near-infrared radiation A, R, P from the first and second lasers 6, 8, and the frequency shifter 12 are directed through the input window 10 of the vapour cell 2 so as to be incident upon the atomic ensemble 4.

(18) The optical or near-infrared radiation P from the second laser 8 (having a Rabi frequency .sub.p) excites atomic valence electrons in the atomic ensemble from their ground state |1> into an intermediate excited state |2> via an electric dipole transition. The frequency of the optical or near-infrared radiation P from the second laser 8 is chosen to be resonant with the atomic transition from the ground state |1> to the intermediate excited state |2>.

(19) The shifted optical or near-infrared radiation R from the first laser 6 (having a Rabi frequency .sub.R) excites atomic valence electrons in the atomic ensemble from their intermediate excited state |2> into a highly excited first Rydberg state |3> via an electric dipole transition. The frequency of the shifted optical or near-infrared radiation R from the first laser 6 is chosen to be resonant with the atomic transition from the intermediate excited state |2> to the first Rydberg state |3>.

(20) Likewise, the optical or near-infrared radiation A from the first laser 6 (having a Rabi frequency .sub.A) excites atomic valence electrons in the atomic ensemble from another excited state |6> to another highly excited third Rydberg state |5> via an electric dipole transition. The frequency of the optical or near-infrared radiation A from the first laser 6 is chosen to be detuned from the atomic transition from the excited state |6> to the third Rydberg state |5> by an amount .sub.5-.sub.6.

(21) The microwave or terahertz radiation generator 14 is also energised to produce microwave or terahertz radiation C that is directed along the waveguide 18 and through the input window 16 of the vapour cell 2 so as also to be incident upon the atomic ensemble 4. This microwave or terahertz radiation C (having a Rabi frequency .sub.C) excites atomic valence electrons from the third Rydberg state |5> to a higher second Rydberg state |4> via an electric dipole transition. The frequency of the microwave or terahertz radiation C is chosen to be detuned from the atomic transition from the third Rydberg state |5> to the second Rydberg state |4> by an amount .sub.4-.sub.5.

(22) With the three sources of optical or near-infrared radiation A, R, P and the source of microwave or terahertz radiation C incident upon the atomic ensemble 4 in the vapour cell 2, the input electromagnetic radiation can then be input to the atomic ensemble 4 for conversion. The resonant optical or near-infrared radiation R, P (having Rabi frequencies .sub.R and .sub.P respectively) from the first and second lasers 6, 8 respectively create a coherence on the |1>.Math.|3> transition through coherent population trapping.

(23) If the electromagnetic frequency converter 1 is being used to convert microwave or terahertz radiation into optical or near-infrared radiation, the microwave or terahertz radiation M (having a Rabi frequency .sub.M) is input from the microwave or terahertz input 22 and directed along the waveguide 18 and through the input window 16 of the vapour cell 2 so as to be incident upon the atomic ensemble 4. Upon incidence on the atomic ensemble 4, the microwave or terahertz radiation M couples to the electric dipole transition between the Rydberg states |3> and |4>, with the frequency of the input microwave or terahertz radiation M being detuned from the transition |3>.Math.|4> by an amount .sub.4.

(24) When the microwave or terahertz radiation M is input, this creates a coherence on the optical or near-infrared frequency transition |6>.Math.|1>, but not on the microwave or terahertz frequency transition |4>.Math.|3> (which is suppressed through quantum interference). As a result, the input microwave or terahertz radiation M is converted into optical or near-infrared radiation (having a Rabi frequency .sub.L). This optical or near-infrared radiation is then output from the atomic ensemble 4 through the output window 32 in the vapour cell 2 that is transparent to the frequency of the optical or near-infrared radiation, where it is received by the optical or near-infrared radiation output 26.

(25) If the electromagnetic frequency converter 1 is being used to convert optical or near-infrared radiation into microwave or terahertz radiation, the optical or near-infrared radiation L (having a Rabi frequency .sub.L) is input from the optical or near-infrared input 20 and directed through the input window 10 (that is transparent to radiation of such frequency) of the vapour cell 2 so as to be incident upon the atomic ensemble 4. Upon incidence on the atomic ensemble 4, the optical or near-infrared radiation L couples to the electric dipole transition between the ground and excited states |1> and |6>, with the frequency of the input optical or near-infrared radiation L being detuned from the transition |1>.Math.|6> by an amount .sub.6.

(26) When the optical or near-infrared radiation L is input, this creates a coherence on the microwave or terahertz frequency transition |4>.Math.|3>, but not on the optical or near-infrared frequency transition |6>.Math.|1> (which is suppressed through quantum interference). As a result, the input optical or near-infrared radiation L is converted into microwave or terahertz radiation (having a Rabi frequency .sub.M). This microwave or terahertz radiation is then output from the atomic ensemble 4 through the output window 28 in the vapour cell 2 that is transparent to the frequency of the microwave or terahertz radiation, where it is received by the microwave or terahertz radiation output 24 via the output waveguide 30.

(27) As has been described above, while the sources of optical or near-infrared radiation P, R have frequencies that are resonant with the respective atomic transitions, the input optical or near-infrared radiation L, or the input microwave or terahertz radiation M, as well as the source of optical or near-infrared radiation A and the source of optical or near-infrared radiation C are detuned from their respective atomic transitions.

(28) In order for the conversion efficiency of the incident radiation to be maximised, preferably the following conditions between the Rabi frequencies and the detuning parameters are met:

(29) ${}_5=\frac{{.Math.{}_C.Math.}^2}{{}_4};{}_6=\frac{{.Math.{}_A.Math.}^2}{{}_5};\mathrm{and}.Math.{}_R.Math..Math.{}_P.Math.,$
where .sub.C, .sub.A, .sub.R and .sub.P are the Rabi frequencies of the respective sources of electromagnetic radiation C, A, R and P, .sub.4 is the detuning of the frequency of the input microwave or terahertz radiation M from the transition |3>.Math.|4>, .sub.6 is the detuning of the frequency of the input optical or near-infrared radiation L from the transition |1>.Math.|6>, .sub.4-.sub.5 is the detuning of the frequency of the microwave or terahertz radiation C from the atomic transition from the third Rydberg state |5> to the second Rydberg state |4> and .sub.5-.sub.6 is the detuning of the frequency of the optical or near-infrared radiation A from the atomic transition from the excited state |6> to the third Rydberg state |5>.

(30) These detuning conditions enable a quantum interference effect where the atomic ensemble is nearly transparent for the input electromagnetic radiation while generating a coherence on the transition that produces the output electromagnetic radiation. If these conditions are strongly violated, the input electromagnetic radiation experiences dispersion or absorption in the atomic ensemble and may not be converted into the output field. The tolerance in the detunings in order to maximise the efficiency of the conversion is similar to the allowed bandwidth of the input electromagnetic radiation.

(31) FIG. 3 shows an specific example of an atomic level scheme used in an electromagnetic frequency converter according to an embodiment of the present invention, when the vapour cell contains an atomic ensemble of rubidium atoms.

(32) Operation of this embodiment, which may be arranged according to the setup shown in FIG. 1, will now be described. Similar to the embodiment described with reference to FIGS. 1 and 2, the embodiment shown in FIG. 3 is able to operate in two main modes of operation: to convert microwave radiation into near-infrared radiation and vice versa. Both modes of operation will now be described with reference to FIGS. 1 and 3.

(33) In both modes of operation, the atomic ensemble 4 of rubidium atoms is prepared in the vapour cell 2 and the heater is energised to vaporise the rubidium atoms of the atomic ensemble 4. The first laser 6, having a frequency of approximately 625 THz, is energised and a portion of its output radiation (having an intensity of approximately 531 mW/mm.sup.2) is separated from the rest of the laser beam and directed through the frequency shifter 12 to shift its frequency to approximately 632 THz. The remaining 625 THz radiation A (having an intensity of approximately 455 mW/mm.sup.2) and the 632 THz radiation R from the first laser 6 are directed through the input window 10 of the vapour cell 2 so as to be incident upon the rubidium atomic ensemble 4.

(34) The electromagnetic radiation P from the second laser 8, having a frequency of approximately 377 THz and an intensity of approximately 2.3 W/mm.sup.2, is also directed through the input window 10 of the vapour cell 2 so as to be incident upon the rubidium atomic ensemble 4.

(35) The 377 THz radiation P from the second laser 8 excites atomic valence electrons in the atomic ensemble from their 5S.sub.1/2 ground state into an intermediate 5P.sub.1/2 excited state via an electric dipole transition. The 377 THz radiation P is resonant with the atomic transition from the 5S.sub.1/2 ground state to the intermediate 5P.sub.1/2 excited state.

(36) The shifted 632 THz radiation R from the first laser 6 excites atomic valence electrons in the atomic ensemble from their intermediate 5P.sub.1/2 excited state into a highly excited 30S.sub.1/2 first Rydberg state via an electric dipole transition. The 632 THz radiation R is resonant with the atomic transition from the intermediate 5P.sub.1/2 excited state to the m.sub.J=1/2 Zeeman sublevel of the 30S.sub.1/2 first Rydberg state.

(37) Likewise, the 625 THz radiation A from the first laser 6 excites atomic valence electrons in the atomic ensemble from a 5P.sub.3/2 excited state to the m.sub.J=+1/2 Zeeman sublevel of the excited 30S.sub.1/2 third Rydberg state via an electric dipole transition. The 625 THz radiation A is detuned from the atomic transition from the 5P.sub.3/2 excited state to the m.sub.J=+1/2 Zeeman sublevel of the excited 30S.sub.1/2 third Rydberg state by 36 MHz.

(38) The microwave radiation generator 14 is also energised to produce microwave radiation C, having a frequency of approximately 157 GHz and an intensity of 239 nW/mm.sup.2, that is directed along the waveguide 18 and through the input window 16 of the vapour cell 2 so as also to be incident upon the atomic ensemble 4. This 157 GHz radiation C excites atomic valence electrons from the m.sub.J=+1/2 Zeeman sublevel of the excited 30S.sub.1/2 third Rydberg state to a higher 30P.sub.1/2 second Rydberg state via an electric dipole transition. The 157 GHz radiation C is detuned from the atomic transition from the m.sub.J=+1/2 Zeeman sublevel of the excited 30S.sub.1/2 third Rydberg state to the 30P.sub.1/2 second Rydberg state by 48 MHz at each end of the transition.

(39) With the 377 THz radiation P, the 632 THz radiation R, the 625 THz radiation A and the 157 GHz radiation C incident upon the rubidium atomic ensemble 4 in the vapour cell 2, the input electromagnetic radiation can then be input to the atomic ensemble 4 for conversion. The 377 THz radiation P and the 632 THz radiation R from the first and second lasers 6, 8 respectively create a coherence on the transition between the 5S.sub.1/2 ground state and the m.sub.J=1/2 Zeeman sublevel of the 30S.sub.1/2 first Rydberg state through coherent population trapping.

(40) If the electromagnetic frequency converter 1 is being used to convert microwave radiation into near-infrared radiation, the microwave radiation M (having a frequency of approximately 157 GHz) is input from the microwave input 22 and directed along the waveguide 18 and through the input window 16 of the vapour cell 2 so as to be incident upon the atomic ensemble 4. Upon incidence on the atomic ensemble 4, the microwave radiation M couples to the electric dipole transition between the m.sub.J=1/2 Zeeman sublevel of the 30S.sub.1/2 first Rydberg state and the 30P.sub.1/2 second Rydberg state (from which it is detuned by 48 MHz).

(41) When the 157 GHz microwave radiation M is input, this creates a coherence on the near-infrared frequency transition between the 5P.sub.3/2 excited state and the 5S.sub.1/2 ground state, but not on the microwave frequency transition between the m.sub.J=1/2 Zeeman sublevel of the 30S.sub.1/2 first Rydberg state and the 30P.sub.1/2 second Rydberg state (which is suppressed through quantum interference). As a result, the input 157 GHz microwave radiation M is converted into near-infrared radiation (having a frequency of approximately 384 THz, which is detuned from the transition between the 5P.sub.3/2 excited state and the 5S.sub.1/2 ground state by 12 MHz). This 384 THz near-infrared radiation is then output from the atomic ensemble 4 through the output window 32 in the vapour cell 2 that is transparent to the 384 THz near-infrared radiation, where it is received by the near-infrared radiation output 26.

(42) If the electromagnetic frequency converter 1 is being used to convert near-infrared radiation into microwave radiation, the 384 THz near-infrared radiation L (is input from the optical input 20 and directed through the input window 10 (that is transparent to radiation of such frequency) of the vapour cell 2 so as to be incident upon the atomic ensemble 4. Upon incidence on the atomic ensemble 4, the 384 THz radiation L couples to the electric dipole transition between the 5P.sub.3/2 excited state and the 5S.sub.1/2 ground state, with the frequency of the 384 THz input radiation L being detuned from the transition by 12 MHz.

(43) When the 384 THz radiation L is input, this creates a coherence on the microwave transition between the m.sub.J=1/2 Zeeman sublevel of the 30S.sub.1/2 first Rydberg state and the 30P.sub.1/2 second Rydberg state, but not on the 384 THz optical transition between the 5P.sub.3/2 excited state and the 5S.sub.1/2 ground state (which is suppressed through quantum interference). As a result, the input 384 THz radiation L is converted into microwave radiation (having a frequency of approximately 157 GHz, which is detuned from the transition between the m.sub.J=1/2 Zeeman sublevel of the 30S.sub.1/2 first Rydberg state and the 30P.sub.1/2 second Rydberg state by 48 MHz). This 157 GHz microwave radiation is then output from the atomic ensemble 4 through the output window 28 in the vapour cell 2 that is transparent to the frequency of the 157 GHz microwave radiation, where it is received by the microwave radiation output 24 via the output waveguide 30.

(44) FIGS. 4 and 4b show simulation plots of the intensities of input electromagnetic radiation frequencies into the embodiment of the electromagnetic frequency converter operated according to the atomic level scheme shown in FIG. 3. The efficiency of the electromagnetic wavelength converter according to the scheme shown in FIG. 3 will now be described with reference to the plots shown in FIGS. 4a and 4b. The dots in the plots indicate the results from a numerical integration of the Maxwell-Bloch equations.

(45) The parameters used in the simulations were:

(46) /=1/624.84, where is the lifetime of the 30S.sub.1/2 first Rydberg state, and is the lifetime of the intermediate 5P.sub.1/2 excited state;

(47) .sub.A=4, where .sub.A is the Rabi frequency of the 625 THz radiation A from the first laser 6;

(48) .sub.C=8, where .sub.C is the Rabi frequency of the 157 GHz radiation C from the microwave generator 14;

(49) .sub.R=3, where .sub.R is the Rabi frequency of the shifted 632 THz radiation R from the first laser 6;

(50) .sub.P=0.15, where .sub.P is the Rabi frequency of the 377 THz radiation P from the second laser 8;

(51) .sub.4=8;

(52) .sub.6=8;

(53) .sub.6=2; and

(54) b=7.24.

(55) The above parameters can be seen to satisfy the detuning conditions:

(56) ${}_5=\frac{{.Math.{}_C.Math.}^2}{{}_4};{}_6=\frac{{.Math.{}_A.Math.}^2}{{}_5};\mathrm{and}.Math.{}_R.Math..Math.{}_P.Math..$
Other quantities used for the simulations for this rubidium level scheme were:

(57) the dipole matrix element on the microwave transition between the m.sub.J=1/2 Zeeman sublevel of the 30S.sub.1/2 first Rydberg state and the 30P.sub.1/2 second Rydberg state is |d.sub.43|=397.83 ea.sub.0, where e is the elementary charge and a.sub.0 is the Bohr radius; and

(58) the dipole matrix element on the near-infrared transition between the 5P.sub.3/2 excited state and the 5S.sub.1/2 ground state is |d.sub.6|=2.99ea.sub.0.

(59) In FIG. 4a, which shows the intensity of the input microwave field and the output near-infrared field as a function of the depth into the atomic ensemble, a continuous wave microwave field 101 (of frequency 157 GHz) enters the atomic ensemble at a depth of z=0, with an intensity at z=0 of 18.7 W/mm.sup.2. Full conversion of the input microwave radiation 101 into near-infrared radiation 102 occurs after a length of I=186.6 I.sub.abs, where I.sub.abs is the absorption length. For an atomic density of =10.sup.17 m.sup.3, the absorption length is I.sub.abs=3.4310.sup.2 mm, so full conversion occurs for I6.4 mm. The conversion efficiency at I=186.6 I.sub.abs is found to be 96.7%. The intensity of the output near-infrared field 102 (of frequency 384 THz) at I=186.6 I.sub.abs is found to be 42.8 nW/mm.sup.2.

(60) As will also be seen from FIG. 4a, after a depth of I=186.6 I.sub.abs into the atomic ensemble, the near-infrared field 102 is converted back into microwave radiation 101.

(61) In FIG. 4b, which shows the intensity of the input near-infrared field and the output microwave field as a function of the depth into the atomic ensemble, a continuous wave near-infrared field 201 (of frequency 384 THz) enters the atomic ensemble at a depth of z=0, with an intensity at z=0 of 331.3 nW/mm.sup.2. Full conversion of the input near-infrared radiation 201 into microwave radiation 202 occurs after a length of I=186.6 I.sub.abs, where I.sub.abs is the absorption length. For an atomic density of =10.sup.17 m.sup.3, the absorption length is I.sub.abs=3.4310.sup.2 mm, so full conversion occurs for I6.4 mm. The conversion efficiency at I=186.6 I.sub.abs is found to be 96.7%. The intensity of the output microwave field 202 (of frequency 157 GHz) at I=186.6 I.sub.ab, is found to be 126.7 W/mm.sup.2.

(62) As will also be seen from FIG. 4b, after a depth of I=186.6 I.sub.abs into the atomic ensemble, the microwave field 202 is converted back into near-infrared radiation 201.

(63) FIG. 5 shows another specific example of an atomic level scheme used in an electromagnetic frequency converter according to an embodiment of the present invention, when the vapour cell contains an atomic ensemble of rubidium atoms, but using different transitions to the scheme shown in FIG. 3.

(64) This embodiment may be implemented according to the setup shown in FIG. 1, however preferably all of the fields (i.e. both the optical and the microwave (or terahertz) fields are co-propagating. Thus, in this embodiment, the input waveguide 18 is positioned to input the microwave or terahertz radiation M from the microwave or terahertz input 22 through the same input window 10 as the optical or near-infrared radiation L. Also, the output waveguide 30 is positioned to receive the output microwave or terahertz radiation from the same output window 32 as the output optical or near-infrared radiation L. Thus in this embodiment the input window 10 and the output window 32 are transparent to the frequencies of the microwave or terahertz radiation and to the frequencies of the optical or near-infrared radiation that are used.

(65) Similar to the embodiment described with reference to FIGS. 1 and 2, the embodiment shown in FIG. 4 is able to operate in two main modes of operation: to convert terahertz radiation into near-infrared radiation and vice versa. Both modes of operation will now be described with reference to FIGS. 1 and 4.

(66) In both modes of operation, the atomic ensemble 4 of rubidium atoms is prepared in the vapour cell 2 and the heater is energised to vaporise the rubidium atoms of the atomic ensemble 4. The first laser 6, having a frequency of approximately 617 THz, is energised and a portion of its output radiation (having an intensity of approximately 2.27 W/mm.sup.2) is separated from the rest of the laser beam and directed through the frequency shifter 12 to shift its frequency to approximately 625 THz. The remaining 617 THz radiation A (having an intensity of approximately 2.27 W/mm.sup.2) and the 625 THz radiation R from the first laser 6 are directed through the input window 10 of the vapour cell 2 so as to be incident upon the rubidium atomic ensemble 4.

(67) The electromagnetic radiation P from the second laser 8, having a frequency of approximately 377 THz and an intensity of approximately 5.95 W/mm.sup.2, is also directed through the input window 10 of the vapour cell 2 so as to be incident upon the rubidium atomic ensemble 4.

(68) The 377 THz radiation P from the second laser 8 excites atomic valence electrons in the atomic ensemble from their 5S.sub.1/2 ground state into an intermediate 5P.sub.1/2 excited state via an electric dipole transition. The 377 THz radiation P is resonant with the atomic transition from the 5S.sub.1/2 ground state to the intermediate 5P.sub.1/2 excited state.

(69) The shifted 625 THz radiation R from the first laser 6 excites atomic valence electrons in the atomic ensemble from their intermediate 5P.sub.1/2 excited state into a highly excited 23S.sub.1/2 first Rydberg state via an electric dipole transition. The 625 THz radiation R is resonant with the atomic transition from the intermediate 5P.sub.1/2 excited state to the m.sub.J=1/2 Zeeman sublevel of the 23S.sub.1/2 first Rydberg state.

(70) Likewise, the 617 THz radiation A from the first laser 6 excites atomic valence electrons in the atomic ensemble from a 5P.sub.3/2 excited state to the m.sub.J=+1/2 Zeeman sublevel of the excited 22S.sub.1/2 third Rydberg state via an electric dipole transition. The 617 THz radiation A is detuned from the atomic transition from the 5P.sub.3/2 excited state to the m.sub.J=+1/2 Zeeman sublevel of the excited 22S.sub.1/2 third Rydberg state by 12.1 MHz at each end of the transition.

(71) The terahertz radiation generator 14 is also energised to produce terahertz radiation C, having a frequency of approximately 2.03 THz and an intensity of 12 W/mm.sup.2, that is directed along the waveguide 18 and through the input window 10 of the vapour cell 2 so as also to be incident upon the atomic ensemble 4. This 2.03 THz radiation C excites atomic valence electrons from the m.sub.J=+1/2 Zeeman sublevel of the excited 22S.sub.1/2 third Rydberg state to a higher 24P.sub.1/2 second Rydberg state via an electric dipole transition. The 2.03 THz radiation C is detuned from the atomic transition from the m.sub.J=+1/2 Zeeman sublevel of the excited 22S.sub.1/2 third Rydberg state to the 24P.sub.1/2 second Rydberg state by 12.1 MHz at each end of the transition.

(72) With the 377 THz radiation P, the 625 THz radiation R, the 617 THz radiation A and the 2.03 THz radiation C incident upon the rubidium atomic ensemble 4 in the vapour cell 2, the input electromagnetic radiation can then be input to the atomic ensemble 4 for conversion. The 377 THz radiation P and the 625 THz radiation R from the first and second lasers 6, 8 respectively create a coherence on the transition between the S.sub.1/2 ground state and the m.sub.J=1/2 Zeeman sublevel of the 23S.sub.1/2 first Rydberg state through coherent population trapping. If the electromagnetic frequency converter 1 is being used to convert terahertz radiation into near-infrared radiation, the terahertz radiation M (having a frequency of approximately 1.12 THz) is input from the terahertz input 22 and directed along the waveguide 18 and through the input window 10 of the vapour cell 2 so as to be incident upon the atomic ensemble 4. Upon incidence on the atomic ensemble 4, the terahertz radiation M couples to the electric dipole transition between the m.sub.J=1/2 Zeeman sublevel of the 23S.sub.1/2 first Rydberg state and the 24P.sub.1/2 second Rydberg state (from which it is detuned by 12.1 MHz).

(73) When the 1.12 THz terahertz radiation M is input, this creates a coherence on the near-infrared frequency transition between the 5P.sub.3/2 excited state and the S.sub.1/2 ground state, but not on the terahertz frequency transition between the m.sub.J=1/2 Zeeman sublevel of the 23S.sub.1/2 first Rydberg state and the 24P.sub.1/2 second Rydberg state (which is suppressed through quantum interference). As a result, the input 1.12 THz terahertz radiation M is converted into near-infrared radiation (having a frequency of approximately 384 THz, which is detuned from the transition between the 5P.sub.3/2 excited state and the S.sub.1/2 ground state by 12.1 MHz). This 384 THz near-infrared radiation is then output from the atomic ensemble 4 through the output window 32 in the vapour cell 2 that is transparent to the 384 THz near-infrared radiation, where it is received by the near-infrared radiation output 26.

(74) If the electromagnetic frequency converter 1 is being used to convert near-infrared radiation into terahertz radiation, the 384 THz near-infrared radiation L (is input from the optical input 20 and directed through the input window 10 (that is transparent to radiation of such frequency) of the vapour cell 2 so as to be incident upon the atomic ensemble 4. Upon incidence on the atomic ensemble 4, the 384 THz radiation L couples to the electric dipole transition between the 5P.sub.3/2 excited state and the S.sub.1/2 ground state, with the frequency of the 384 THz input radiation L being detuned from the transition by 12.1 MHz.

(75) When the 384 THz radiation L is input, this creates a coherence on the terahertz transition between the m.sub.J=1/2 Zeeman sublevel of the 23S.sub.1/2 first Rydberg state and the 24P.sub.1/2 second Rydberg state, but not on the 384 THz optical transition between the 5P.sub.3/2 excited state and the S.sub.1/2 ground state (which is suppressed through quantum interference). As a result, the input 384 THz radiation L is converted into terahertz radiation (having a frequency of approximately 1.12 THz, which is detuned from the transition between the m.sub.J=1/2 Zeeman sublevel of the 23S.sub.1/2 first Rydberg state and the 24P.sub.1/2 second Rydberg state by 12.1 MHz). This 1.12 THz terahertz radiation is then output from the atomic ensemble 4 through the output window 32 in the vapour cell 2 that is transparent to the frequency of the 1.12 THz terahertz radiation, where it is received by the terahertz radiation output 24 via the output waveguide 30.

(76) FIGS. 6 and 6b show simulation plots of the intensities of input electromagnetic radiation frequencies into the embodiment of the electromagnetic frequency converter operated according to the atomic level scheme shown in FIG. 5. The efficiency of the electromagnetic wavelength converter according to the scheme shown in FIG. 5 will now be described with reference to the plots shown in FIGS. 6a and 6b. The dots in the plots indicate the results from a numerical integration of the Maxwell-Bloch equations.

(77) The parameters used in the simulations were:

(78) /=1/285, where is the lifetime of the 23S.sub.1/2 first Rydberg state, and is the lifetime of the intermediate 5P.sub.1/2 excited state;

(79) .sub.A=2, where .sub.A is the Rabi frequency of the 617 THz radiation A from the first laser 6;

(80) .sub.C=2, where .sub.C is the Rabi frequency of the 1.12 THz radiation C from the terahertz generator 14;

(81) .sub.R=2, where .sub.R is the Rabi frequency of the shifted 625 THz radiation R from the first laser 6;

(82) .sub.P=0.3, where .sub.P is the Rabi frequency of the 377 THz radiation P from the second laser 8;

(83) .sub.4=2;

(84) .sub.6=2;

(85) .sub.6=2; and

(86) b=0.72.

(87) The above parameters can be seen to satisfy the detuning conditions:

(88) ${}_5=\frac{{.Math.{}_C.Math.}^2}{{}_4};{}_6=\frac{{.Math.{}_A.Math.}^2}{{}_5};\mathrm{and}.Math.{}_R.Math..Math.{}_P.Math..$
Other quantities used for the simulations for this rubidium level scheme were:

(89) the dipole matrix element on the terahertz transition between the m.sub.J=1/2 Zeeman sublevel of the 23S.sub.1/2 first Rydberg state and the 24P.sub.1/2 second Rydberg state is |d.sub.43|=27.03ea.sub.0, where e is the elementary charge and a.sub.0 is the Bohr radius; and the dipole matrix element on the near-infrared transition between the 5P.sub.3/2 excited state and the S.sub.1/2 ground state is |d.sub.61|=1.73 ea.sub.0.

(90) In FIG. 6a, which shows the intensity of the input terahertz field and the output near-infrared field as a function of the depth into the atomic ensemble, a continuous wave terahertz field 301 (of frequency 1.12 THz) enters the atomic ensemble at a depth of z=0, with an intensity at z=0 of 40.5 W/mm.sup.2. Full conversion of the input terahertz radiation 301 into near-infrared radiation 302 occurs after a length of I=100 I.sub.abs, where I.sub.abs is the absorption length. For an atomic density of =210.sup.17 m.sup.3, the absorption length is I.sub.abs=5.110.sup.2 mm, so full conversion occurs for I5.1 mm. The conversion efficiency at I=100 I.sub.abs is found to be 92.1%. The intensity of the output near-infrared field 302 (of frequency 384 THz) at I=100 I.sub.abs is found to be 11.8 nW/mm.sup.2.

(91) As will also be seen from FIG. 6a, after a depth of I=100 I.sub.abs into the atomic ensemble, the near-infrared field 302 is converted back into terahertz radiation 301.

(92) In FIG. 6b, which shows the intensity of the input near-infrared field and the output terahertz field as a function of the depth into the atomic ensemble, a continuous wave near-infrared field 401 (of frequency 384 THz) enters the atomic ensemble at a depth of z=0, with an intensity at z=0 of 9.94 nW/mm.sup.2. Full conversion of the input near-infrared radiation 401 into terahertz radiation 402 occurs after a length of I=100 I.sub.abs, where I.sub.abs is the absorption length. For an atomic density of =210.sup.17 m.sup.3, the absorption length is I.sub.abs=5.110.sup.2 mm, so full conversion occurs for I5.1 mm. The conversion efficiency at I=100 I.sub.abs is found to be 92.1%. The intensity of the output terahertz field 402 (of frequency 1.12 THz) at I=100 I.sub.abs is found to be 24.5 W/mm.sup.2.

(93) As will also be seen from FIG. 6b, after a depth of I=100 I.sub.abs into the atomic ensemble, the terahertz field 402 is converted back into near-infrared radiation 401.

(94) It can be seen from the above that in at least preferred embodiments of the invention, an electromagnetic frequency converter is provided that offers an efficient frequency conversion mechanism between optical or near-infrared radiation and microwave or terahertz frequency radiation (or vice versa). Such a converter does not require the use of a cavity, thus offering a greater bandwidth for conversion frequencies. Furthermore, the converter does not require any optical pumping because the highly excited Rydberg states are unpopulated at room temperature so there is no thermal noise to suppress, and does not require any micro-fabrication of components because the active component of the converter is simply a volume of atoms to which radiation is applied.

(95) Although the embodiments shown in the Figures use four drive fields, i.e. three optical or near-infrared fields and one microwave field, to perform the conversion, it will be appreciated that the transition from the ground state |1> to the first Rydberg state |3> may be performed using only a single drive field or using three or more drive fields via two or more intermediate states through respective transitions. Similarly, the transition from the excited state |6> to the second Rydberg state |4> may be performed using only a single drive field or using three or more drive fields via two or more intermediate states through respective transitions.

(96) The work leading to this invention has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. 319286. The support of the National University of Singapore with this work is also acknowledged.