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Journal of Physics Conference Series

Squeezing of a quantum flux in a double rf-SQUID system

Kohji Takashima, Shigemasa Matsuo, Toshiyuki Fujii, Noriyuki Hatakenaka, Susumu Kurihara, Anton Zeilinger

Published Mar 1, 2009• 7 citations
Publisher

Abstract

We investigate the nonstationary boundary effect for a quantum flux in a double rf-SQUID system. In a superconducting ring interrupted by a dc-SQUID (so-called double rf-SQUID), the Josephson potential can be controlled by the magnetic flux through the dc-SQUID ring. This system is equivalent to an anharmonic oscillator with a time-dependent frequency. A rapid change of the magnetic flux in the dc-SQUID leads to the nonadiabatic mixing of the quantum states for a quantum flux in a double rf-SQUID. Therefore, this becomes a circuit analogue of the dynamical Casimir effect in quantum field theory. We perform numerical calculations for the quantum state evolution of the quantum flux within a harmonic approximation, taking account of the nonadiabatic effect. We found that the resulting state distribution has a super-Poissonian character that reflects flux squeezing caused by the Bogoliubov transformation between eigenstates at different times.

DOI
10.1088/1742-6596/150/5/052260

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We investigate the nonstationary boundary effect for a quantum flux in a double rf-SQUID system. In a superconducting ring interrupted by a dc-SQUID (so-called double rf-SQUID), the Josephson potential can be controlled by the magnetic flux through the dc-SQUID ring. This system is equivalent to an anharmonic oscillator with a time-dependent frequency. A rapid change of the magnetic flux in the dc-SQUID leads to the nonadiabatic mixing of the quantum states for a quantum flux in a double rf-SQUID. Therefore, this becomes a circuit analogue of the dynamical Casimir effect in quantum field theory. We perform numerical calculations for the quantum state evolution of the quantum flux within a harmonic approximation, taking account of the nonadiabatic effect. We found that the resulting state distribution has a super-Poissonian character that reflects flux squeezing caused by the Bogoliubov transformation between eigenstates at different times.
We investigate a quantum-circuit analog of the dynamical Casimir effect discussed in cavity quantum electrodynamics (QED). A double superconducting quantum interference device (SQUID), consisting of a superconducting loop interrupted by a dc-SQUID, is regarded as a harmonic oscillator with a time-dependent frequency imitating the nonadiabatic boundaries in a cavity QED. Squeezing occurs due to parametric processes inherent in the system. We reformulate squeezing based on the Bogoliubov transformation between eigenstates at different times and derive the analytic formula for quantum-state evolutions of the system. The squeezing parameter clearly reveals the relationship between squeezing and nonadiabatic nature of the system. Thus, the squeezing parameter serves as a measure for the dynamical Casimir effect. We demonstrate squeezing for two types of frequency modulation and propose a method for measuring squeezing by using a circuit QED technique under coherent oscillations between an artificial atom and an LC circuit in the presence of dissipation. These observations suggest that a quantum circuit with a Josephson junction is a promising candidate for detecting the dynamical Casimir effect.
Conventional rf SQUIDs (superconducting quantum interference devices) consist of a superconducting loop interrupted by one weak link, and when read out via a tank circuit they produce output signals in the order of a few tens of microvolts. When the single weak link is replaced by a dc SQUID (a superconducting loop with two junctions) a so-called double quantization loop SQUID is formed. In this paper it is shown theoretically, and supported experimentally with thin-film devices of three different designs, that the general behaviour can be explained by a simplified picture of the fixed critical current of the single junction of the rf SQUID being replaced by an effective critical current of a dc SQUID loop that is varied by the applied magnetic flux (i.e., we have a rf SQUID with a variable β parameter). A more detailed analysis of the experimental data and the theory of this novel device reveals its interesting nonlinear character and shows the deviations from this simple picture. It is demonstrated experimentally that output signals in the order of ≥1 mV can be obtained with a suitable read-out mode for the tank circuit, a clear advantage when compared to conventional rf SQUIDs. With respect to dc SQUIDs, the coupling to integrated planar input coils will be unproblematic since no microwave resonances should occur in the structures.
At an extremely low temperature of 20 mK, we measured the loop current in a tunable rf superconducting quantum interference device (SQUID) with a dc-SQUID. By adjusting the magnetic flux applied to the rf-SQUID loop (Φ f ) and the small dc-SQUID (Φ cjj f ), respectively, the potential shape of the system can be fully controlled in situ. Variation in the transition step and overlap size in the switching current with a barrier flux bias are analyzed, from which we can obtain some relevant device parameters and build a model to explain the experimental phenomenon.
At an extremely low temperature of 20 mK, we measured the loop current in a tunable rf superconducting quantum interference device (SQUID) with a dc-SQUID. By adjusting the magnetic flux applied to the rf-SQUID loop ( Φ f ) and the small dc-SQUID ( Φ f cjj ), respectively, the potential shape of the system can be fully controlled in situ . Variation in the transition step and overlap size in the switching current with a barrier flux bias are analyzed, from which we can obtain some relevant device parameters and build a model to explain the experimental phenomenon.
We proposed a quantum-circuit analog of dynamical Casimir effect by using a superconducting quantum circuit. The proposed system can be regarded as a time-dependent harmonic oscillator, resulting in squeezing of a quantum flux trapped in the system. Here we develop our theory taking into account finite temperatures, in order to contact with experiments like circuit-QED. We present numerical results of occupation probability distributions produced by non-stationary boundary effect at various temperatures.