DIPOLE ELEMENT FOR SUPERCONDUCTING CIRCUITS

Abstract

The present invention relates to an inductive dipole element for a superconducting microwave quantum circuit. The dipole element comprises a DC-SQUID formed by a pair of Josephson junctions shunted by an inductance, wherein the Josephson junctions have equal energy, and the Josephson junctions and the inductance are arranged such that each of the junctions forms a loop with the inductance. The two loops are asymmetrically threaded with external magnetic DC fluxes φ.sub.ext1 and φ.sub.ext2, respectively, such that φ.sub.ext1=π and φ.sub.ext2=0, wherein parametric pumping is enabled by modulating the total flux φ.sub.Σ=φ.sub.ext,1+φ.sub.ext,2 threading the dipole element, thereby allowing even-wave mixing between modes that participate in the dipole element with no Kerr-like interactions.

Claims

1. An inductive dipole element for a superconducting microwave quantum circuit, the dipole element comprising a DC-SQUID formed by a pair of Josephson junctions shunted by an inductance, wherein the Josephson junctions have equal energy, and the Josephson junctions and the inductance are arranged such that each of the junctions forms a loop with the inductance, the two loops being asymmetrically threaded with external magnetic DC fluxes φ.sub.ext1 and φ.sub.ext2, respectively, such that φ.sub.ext1=π and φ.sub.ext2=0, wherein parametric pumping is enabled by modulating the total flux φ.sub.Σ=φ.sub.ext,1+φ.sub.ext,2 threading the dipole element, thereby allowing even-wave mixing between modes that participate in the dipole element with no Kerr-like interactions.

2. The dipole element according to claim 1, wherein the parametric pumping is further enabled by modulating also φ.sub.Δ=φ.sub.ext,1−φ.sub.ext,2 with an appropriate modulation phase and amplitude.

3. The dipole element according to claim 1, wherein the external magnetic DC fluxes φ.sub.ext,1 and φ.sub.ext,2 are applied via superconducting lines that are adjacent to the superconducting loops, in which both a DC and an AC current circulate.

4. The dipole element according to claim 3, wherein the superconducting lines are directly connected to wires of the loops.

5. The dipole element according to claim 3, wherein the superconducting lines are arranged such that one input current I.sub.Σ biases the total flux in the dipole element, φ.sub.Σ=φ.sub.ext,1+φ.sub.ext,2, and another input current I.sub.Δ biases the differential flux of the dipole element, φ.sub.Δ=φ.sub.ext,1−φ.sub.ext,2, and wherein the parametric pumping is delivered by the oscillating magnetic flux generated by the oscillating component of I.sub.Σ.

6. The dipole element according to claim 1, wherein the inductance comprises a superconducting wire made of plain or granular superconducting material.

7. The dipole element according to claim 1, wherein the inductance comprises a chain of Josephson junctions connected in series with each other.

8. The dipole element according to claim 1, wherein one of the junctions is replaced by a DC-SQUID to account for natural asymmetries of the junction energies.

9. A superconducting microwave quantum circuit, comprising a dipole element according to claim 1, the dipole element being capacitively shunted to form a non-linear resonator coupled to a linear resonator, wherein the non-linear interaction provided by the parametrically pumped dipole element causes a two-to-one photon exchange between the linear resonator and the non-linear resonator.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Other advantages and features of the invention will become apparent by reference to the following detailed description of illustrative embodiments thereof, and from the accompanying drawings, wherein:

[0028] FIG. 1a-FIG. 1d schematically depict examples of inductive dipoles comprising Josephson junctions;

[0029] FIG. 1e schematically depicts a dipole element in accordance with an illustrative embodiment of the invention;

[0030] FIG. 2 shows an optical image of an asymmetrically threaded DC-SQUID in accordance with an illustrative embodiment of the invention; and

[0031] FIG. 3 depicts a circuit diagram of an ATS dipole in a practical implementation in accordance with an illustrative embodiment of the invention.

DETAILED DESCRIPTION

[0032] It is well understood that the embodiments which will be described hereinafter are in no way limitative. Variants of the invention can be considered comprising only a selection of the characteristics described hereinafter, in isolation from the other characteristics described, if this selection of characteristics is sufficient to confer a technical advantage or to differentiate the invention with respect to the state of the prior art. This selection comprises at least one, preferably functional, characteristic without structural details, or with only a part of the structural details if this part alone is sufficient to confer a technical advantage or to differentiate the invention with respect to the state of the prior art.

[0033] In particular, all the variants and all the embodiments described can be combined together if there is no objection to this combination from a technical point of view.

[0034] In the Figures, the elements that are common to several Figures keep the same reference.

[0035] FIGS. 1a to 1e represent several non-linear inductive dipoles using Josephson junctions. The phase difference across the dipole is denoted φ and corresponds to the time integral of the voltage.

[0036] FIG. 1a shows a simple junction with energy E.sub.J cos(φ), where E.sub.J is the Josephson junction energy and φ is the phase difference across the junction.

[0037] FIG. 1b represents a DC-SQUID with energy 2E.sub.J cos(φ.sub.ext)cos(φ) where the external flux φ.sub.ext is provided by a coil powered by a current source. A DC-SQUID may be seen as a single Josephson junction with tunable energy E.sub.J.Math.2E.sub.J cos(φ.sub.ext).

[0038] FIG. 1c corresponds to an RF-SQUID, and FIG. 1d represents a SNAIL element. Both elements require a flux biasing circuit (current source and coil) to thread external flux through the loops.

[0039] FIG. 1e is a schematic representation of a configuration of a dipole element according to an embodiment of the present invention.

[0040] The dipole element, or Asymmetrically Threaded SQUID (ATS) as represented in FIG. 1e, comprises a pair of Josephson junctions 2, 3 arranged in parallel and forming a loop. According to the represented example, the dipole is symmetric, meaning that the Josephson junctions 2, 3 have identical Josephson energies.

[0041] The loop 5 of the dipole element is shunted (electrically coupled in parallel) in its middle with an inductance 4. The inductance 4 thus delimits two loops, each containing a Josephson junction 2, 3. The dipole according to embodiments disclosed herein thus comprises the two loops 6, 8 formed by the Josephson junctions 2, 3 and the inductance 4.

[0042] According to alternative embodiments, the inductance 4 may be constituted by a chain of Josephson junctions, by a plain superconducting line or made out of granular aluminium, or by any other inductive device adapted for the implementation with the dipole of the present invention.

[0043] The dipole element is biased by a DC magnetic field which threads a flux φ.sub.ext,1 in the first loop 6 and a flux φ.sub.ext,2 in the second loop 8. When the bias is such that φ.sub.ext,1=π and φ.sub.ext,2=0, the dipole has an energy of the form E.sub.Lφ.sup.2/2+2E.sub.J sin φ.sub.Σ sin φ where φ.sub.Σ is a small deviation of the total flux threading the ATS. When the pump couples to φ.sub.Σ such that φ.sub.Σ=φ.sub.p(p+p.sup.+), there are only even terms in the expansion of the dipole energy but none is of the Kerr form. Eventually, the desired mixing term can be selected by adjusting the pump frequency. This dipole enables to engineer any even-wave mixing process, one of the wave being the pump. Another advantage of the ATS is that it has an unbounded potential which makes it better suited for parametric pumping.

[0044] The unbounded potential provided by the central inductance 4, E.sub.Lφ.sup.2/2, prevents the system from escaping to high energy states when the system is strongly pumped. This property enables the ATS according to embodiments disclosed herein to be used for sensitive parametric pumping tasks, such as stabilizing quantum states of coupled electromagnetic modes to form long-lived qubits.

[0045] Thus, the ATS dipole according to embodiments of the present invention circumvents the problems that may arise in the presence of Kerr non-linearity by cancelling these terms by symmetry.

[0046] Crucially, the dipole elements and the parametric pumping should preserve the ATS symmetries according to the present invention. In particular, a small asymmetry in the energy of the junctions that arises from unavoidable fabrication imprecisions, leads to parasitic Kerr nonlinearities.

[0047] In order to compensate for this asymmetry, at least one of the junctions 2, 3 can be made flux tunable by being itself replaced by a SQUID.

[0048] In an embodiment, two neighbouring superconducting lines represented by coils 7, 9 enable to flux bias the circuit. When currents I.sub.1 and I.sub.2 flow through these lines, external fluxes φ.sub.ext,1 and φ.sub.ext,2 thread the two loops of the ATS respectively. The current sources have both, a DC component to set the working point of the ATS and an AC component at the pump frequency to make the desired mixing process resonant. The symmetry of the modulation is achieved by controlling the relative amplitude and phase of the two AC components of the currents I.sub.1 and I.sub.2. Considering the energy of the dipole written in the previous paragraph, the ideal modulation only addresses the total flux φ.sub.Σ=φ.sub.ext,1+φ.sub.ext,2 of the ATS. In practice, some corrections should be brought by modulating also the differential flux φ.sub.Δ=φ.sub.ext,1−φ.sub.ext,2. These corrections are required to compensate for the direct drive of the dipole by the pump tone.

[0049] In an alternative embodiment, the superconducting bias lines share an actual inductance with the loop instead of a mutual inductance in the standard mutual inductance equivalent circuit.

[0050] In another embodiment and for practicality, the biasing lines are arranged such that the current sources I.sub.Σ and I.sub.Δ directly address the total flux φ.sub.Σ and the differential flux φ.sub.Δ (see FIG. 2). The superconducting lines that are coupled to the total flux, are used to convey a microwave pump to the ATS in order to create the oscillating total magnetic flux that acts as a pumping parameter (contrary to φ.sub.Δ which is only required for corrections).

[0051] According to this embodiment, the symmetry of the modulation is achieved by having an on-chip hybrid (equally split transmission line) that allows the pump to only address φ.sub.Σ.

[0052] FIG. 2 shows an optical image of an asymmetrically threaded DC-SQUID in accordance with an illustrative embodiment of the invention. The electromagnetic dipole is fabricated on-chip and arranged within a superconducting circuit (partially shown). In the embodiment of FIG. 2, the shunt inductance 4 separating the two loops each containing a Josephson junction 2, 3 is formed of a chain or array of 5 Josephson junctions (represented by the 5 crosses centred between the pair of identical Josephson junctions 2, 3 forming the SQUID). The left and right flux lines 10, 11 are connected to the same input through an on-chip hybrid (not represented).

[0053] The lines carry the microwave frequency pump and a DC current I.sub.Σ, which thread both loops with a total flux φ.sub.Σ. The flux line 12 at the bottom of the image carries current I.sub.Δ and threads each loop with flux ±φ.sub.Δ. Combining these two controls, the ATS is biased at the π/0 asymmetric DC working point, meaning that φ.sub.ext1−φ.sub.ext2=φ.sub.ext1+φ.sub.ext2=π, with φ.sub.ext1,2 the external flux threading the two loops, respectively. The ATS is operated by modulating the flux φ.sub.Σ with an oscillating magnetic flux at frequency ω.sub.p.

[0054] An example configuration of a superconducting quantum circuit implementing the ATS according to embodiments disclosed herein is represented in FIG. 3. The ATS may be implemented in a circuit to realize a four-wave mixing interaction, one of the waves being a pump tone, the frequency of which being chosen to make the interaction resonant. In particular, the ATS may be implemented for engineering a two-to-one photon exchange interaction between two microwave resonators.

[0055] With reference to FIG. 3, the ATS dipole is shunted with a capacitive device 13, thus forming a resonant mode 20. This nonlinear resonator 20 dubbed the buffer is capacitively coupled 14 to a linear resonator 30 called the storage mode, which is modelled by an LC-circuit (inductance 15, capacitor 16).

[0056] The ATS is pumped at a frequency ω.sub.p=2ω.sub.a−ω.sub.b, where ω.sub.a,b are the frequencies of the storage resonator 30 and the buffer resonator 20, respectively. This parametric pumping mediates a two-to-one photon exchange interaction between the two modes. The storage and buffer modes resonate in the GHz range.

[0057] Such an exchange interaction is of great importance in applications tending towards quantum computing and quantum error correction. For example, the interaction may be used for the stabilization of a new type of qubits, called cat-qubits. Cat-qubits are promising candidates for hardware efficient quantum error correction, allowing for the protection and stabilization of quantum information.

[0058] The dipole according to embodiments disclosed herein may also be implemented for microwave photo-detection applications or for the realization of logical operations between qubits.

[0059] While this invention has been described in conjunction with a number of embodiments, it is evident that many alternatives, modifications, and variations would be or are apparent to those of ordinary skill in the applicable arts. Accordingly, it is intended to embrace all such alternatives, modifications, equivalents, and variations that are within the spirit and scope of this invention.