An embodiment of an optical lattice clock comprising atoms and a laser light source at an operational magic frequency is provided. The atoms are capable of making a clock transition between two levels of electronic states, and the laser light source generates at least a pair of counterpropagating laser beams, each of which having a lattice-laser intensity I. The pair of counterpropagating laser beams forms an optical lattice potential for trapping the atoms at around antinodes of a standing wave created by it. The operational magic frequency is one of the frequencies that have an effect of making lattice-induced clock shift of the clock transition insensitive to variation ΔI of the lattice-laser intensity I, the lattice-induced clock shift being a shift in a frequency for the clock transition of the atoms caused by the variation ΔI of the lattice-laser intensity I.

An embodiment of an optical lattice clock comprising atoms and a laser light source at an operational magic frequency is provided. The atoms are capable of making a clock transition between two levels of electronic states, and the laser light source generates at least a pair of counterpropagating laser beams, each of which having a lattice-laser intensity I. The pair of counterpropagating laser beams forms an optical lattice potential for trapping the atoms at around antinodes of a standing wave created by it. The operational magic frequency is one of the frequencies that have an effect of making lattice-induced clock shift of the clock transition insensitive to variation ΔI of the lattice-laser intensity I, the lattice-induced clock shift being a shift in a frequency for the clock transition of the atoms caused by the variation ΔI of the lattice-laser intensity I.

Methods of using vapor cells may involve providing a vapor cell including a body defining a cavity within the body. At least a portion of at least one surface of the vapor cell within the cavity may include at least one pore having an average dimension of about 500 microns or less, as measured in a direction parallel to the at least one surface. A vapor pressure of a subject material within the cavity may be controlled utilizing the at least one pore by inducing an exposed surface of a subject material in a liquid state within the at least one pore to have a shape different than a shape the exposed surface of the subject material in a liquid state would have on a flat, nonporous surface.

Methods of using vapor cells may involve providing a vapor cell including a body defining a cavity within the body. At least a portion of at least one surface of the vapor cell within the cavity may include at least one pore having an average dimension of about 500 microns or less, as measured in a direction parallel to the at least one surface. A vapor pressure of a subject material within the cavity may be controlled utilizing the at least one pore by inducing an exposed surface of a subject material in a liquid state within the at least one pore to have a shape different than a shape the exposed surface of the subject material in a liquid state would have on a flat, nonporous surface.

An optical lattice clock includes a clock transition space having disposed therein an atom group trapped in an optical lattice, and a triaxial magnetic field correction coil for correcting the magnetic field of the clock transition space. Additionally, in a correction space that includes the clock transition space and is larger than the clock transition space, a photoreceiver promotes the clock transition of the atom group trapped in the optical lattice and acquires a clock transition frequency distribution for the correction space. Further, a corrector corrects the magnetic field of the triaxial magnetic field correction coil on the basis of the frequency distribution measured by the photo receiver.

An optical lattice clock includes a clock transition space having disposed therein an atom group trapped in an optical lattice, and a triaxial magnetic field correction coil for correcting the magnetic field of the clock transition space. Additionally, in a correction space that includes the clock transition space and is larger than the clock transition space, a photoreceiver promotes the clock transition of the atom group trapped in the optical lattice and acquires a clock transition frequency distribution for the correction space. Further, a corrector corrects the magnetic field of the triaxial magnetic field correction coil on the basis of the frequency distribution measured by the photo receiver.

In some variations, an interferometric frequency-reference apparatus comprises: an atom source configured to supply neutral atoms; a collimator configured to form a collimated beam of the neutral atoms; one or more probe lasers; and a Doppler laser configured to determine a ground-state population of the neutral atoms. Other variations provide a method of creating a stable frequency reference, comprising: forming a collimated beam of neutral atoms; illuminating the neutral atoms with first and second probe lasers; adjusting the frequencies of the first probe laser and second probe laser using Ramsey spectroscopy to an S.fwdarw.D transition of the neutral atoms; and determining a ground-state population of the neutral atoms with another laser. The interferometric frequency-reference apparatus may provide an optical frequency reference or a microwave frequency reference.

In some variations, an interferometric frequency-reference apparatus comprises: an atom source configured to supply neutral atoms; a collimator configured to form a collimated beam of the neutral atoms; one or more probe lasers; and a Doppler laser configured to determine a ground-state population of the neutral atoms. Other variations provide a method of creating a stable frequency reference, comprising: forming a collimated beam of neutral atoms; illuminating the neutral atoms with first and second probe lasers; adjusting the frequencies of the first probe laser and second probe laser using Ramsey spectroscopy to an S.fwdarw.D transition of the neutral atoms; and determining a ground-state population of the neutral atoms with another laser. The interferometric frequency-reference apparatus may provide an optical frequency reference or a microwave frequency reference.

A system comprises a digital processing circuit, a frequency modulator, an amplitude modulator, and an adder. The digital processing circuit receives an input signal and a correlation signal and generates a frequency tuning parameter and an amplitude modulation parameter. The frequency modulator generates a frequency modulation signal and the correlation signal. The amplitude modulator receives the amplitude modulation parameter and generates an amplitude modulation signal. The adder receives the frequency tuning parameter and the frequency modulation signal and generates a control signal. In some implementations, the system further comprises a DC feedback circuit that receives the input signal and generates a DC compensation signal. In some implementations, the system further comprises a temperature sensor, a temperature compensation circuit, and a second adder.

A system comprises a digital processing circuit, a frequency modulator, an amplitude modulator, and an adder. The digital processing circuit receives an input signal and a correlation signal and generates a frequency tuning parameter and an amplitude modulation parameter. The frequency modulator generates a frequency modulation signal and the correlation signal. The amplitude modulator receives the amplitude modulation parameter and generates an amplitude modulation signal. The adder receives the frequency tuning parameter and the frequency modulation signal and generates a control signal. In some implementations, the system further comprises a DC feedback circuit that receives the input signal and generates a DC compensation signal. In some implementations, the system further comprises a temperature sensor, a temperature compensation circuit, and a second adder.