Controlled Generation of Squeezed States of Microwave Radiation in a Superconducting Resonant Circuit

Superconducting oscillators have been successfully used for quantum control and readout devices in conjunction with superconducting qubits. Also, squeezed states can improve the accuracy of measurements to subquantum, or at least subthermal, levels. Here, we show theoretically how to produce squeezed states of microwave radiation in a superconducting oscillator with tunable parameters. Its resonance frequency can be changed by controlling an rf SQUID inductively coupled to the oscillator. By repeatedly shifting the resonance frequency between any two values, it is possible to produce squeezed and subthermal states of the electromagnetic field in the (0.1–10) GHz range, even when the relative frequency change is small. We propose experimental protocols for the verification of squeezed state generation, and for their use to improve the readout fidelity when such oscillators serve as quantum transducers.

Figure 1

Squeezing of a thermal state, with $k_{B}T=4{\omega }_0$, by repeated frequency shifts, with ${\lambda }_{\max }-1=0.05$. (a) Contour plots of the approximate expression of the Wigner function in the interaction representation [see Eqs. (5, 6, 7)] are shown as a function of the quadrature variables, $x$ and $y$. Clockwise starting from the upper left: initial thermal state, the state after one, two, and ten cycles. The dark background corresponds to $W=0$, and white to $W=0.08$. (b) A schematic frequency-versus-time dependence necessary to produce the results of Fig. 1a. The idle periods $\Delta t$ are chosen to ensure that every fast shift occurs in the same phase with respect to the quadrature coordinates. Here, one must account for the fact that in the Schröedinger representation, the whole phase plane rotates around the origin with the base oscillator frequency ${\omega }_0$. An additional rotation of the Wigner function as a whole during the slow shift can be neglected in comparison, since the additional phase $|\delta \theta |\le 0.5{\omega }_{0}t|{\lambda }_{\max }^2-1|\ll {\omega }_{0}t$.