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Physical Review Letters

Sisyphus Effects in a Microwave-Excited Flux-Qubit Resonator System

J. C. Skinner, Helen Prance, P. B. Stiffell, Robert J. Prance

Published Dec 14, 2010• 8 citations
Publisher

Abstract

Sisyphus amplification, familiar from quantum optics, has recently been reported as a mechanism to explain the enhanced quality factor of a classical resonant (tank) circuit coupled to a superconducting flux qubit. Here we present data from a coupled system, comprising a quantum mechanical rf SQUID (flux qubit) reactively monitored by an ultrahigh quality factor noise driven rf resonator and excited by microwaves. The system exhibits enhancement of the tank-circuit resonance, bringing it significantly closer (within 1%) to the lasing limit, than previously reported results.

DOI
10.1103/physrevlett.105.257002

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Sisyphus amplification, familiar from quantum optics, has recently been reported as a mechanism to explain the enhanced quality factor of a classical resonant (tank) circuit coupled to a superconducting flux qubit. Here we present data from a coupled system, comprising a quantum mechanical rf SQUID (flux qubit) reactively monitored by an ultrahigh quality factor noise driven rf resonator and excited by microwaves. The system exhibits enhancement of the tank-circuit resonance, bringing it significantly closer (within 1%) to the lasing limit, than previously reported results.
A superconducting charge-flux qubit coupled to a high-Q tank circuit was studied in a low-frequency electric field. A fine structure of the multiphoton resonance lines and quantum interference effects associated with the excitation of a quasi-two-level system due to the Landau–Zener–Stückelberg tunneling was observed. The results obtained for multiphoton resonant excitations and low-frequency oscillations of the average occupation of quantum levels were compared using different parameters of the measuring circuit. The mechanism responsible for the fine structure of resonance lines was considered. The method to measure the impedance arising in the tank circuit due to the oscillations of the superconducting current in the qubit and the main sources of decoherence were discussed.
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.
We demonstrate amplification of a microwave signal by a strongly driven two-level system in a coplanar waveguide resonator. The effect, similar to the dressed-state lasing known from quantum optics, is observed with a single quantum system formed by a persistent current (flux) qubit. The transmission through the resonator is enhanced when the Rabi frequency of the driven qubit is tuned into resonance with one of the resonator modes. Amplification as well as linewidth narrowing of a weak probe signal has been observed. The stimulated emission in the resonator has been studied by measuring the emission spectrum. We analyzed our system and found an excellent agreement between the experimental results and the theoretical predictions obtained in the dressed-state model.
Recent experiments on quantum state engineering with superconducting circuits realized concepts originally introduced in the field of quantum optics. Motivated by one such experiment we investigate a Josephson qubit coupled to a slow LC oscillator with frequency much lower than the qubit’s energy splitting. The qubit is ac‐driven to perform Rabi oscillations, and the Rabi frequency is tuned to resonance with the oscillator. The properties of this driven circuit QED system depend strongly on relaxation and decoherence effects in the qubit. We investigate both one‐photon and two‐photon qubit‐oscillator coupling, the latter being dominant at the symmetry point of the qubit. When the qubit driving frequency is blue detuned, we find that the system exhibits lasing behavior; for red detuning the qubit cools the oscillator. Similar behavior is expected in an accessible range of parameters for a Josephson qubit coupled to a nano‐mechanical oscillator. In a different parameter regime, furthering the analogies between superconducting and quantum optical systems, we investigate Sisyphus damping, which is the key element of the Sisyphus cooling protocol, as well as its exact opposite, Sisyphus amplification.
Circuit-QED - the electrical analogue of cavity quantum electrodynamics in atomic physics- is an emerging field of research. By coupling superconducting qubits to an on-chip high-quality resonator it is possible to study a number of effects that are of interest for fundamental tests of quantum mechanics and also have potential applications in quantum information processing, metrology and communication. We have performed computer simulations of a system comprising a flux qubit strongly coupled to a high-quality coplanar waveguide resonator driven by an external microwave source. Using realistic values for the various parameters we have studied, among other things, the transmittance of the cavity and the spectrum of the emitted radiation.
We demonstrate amplification (and attenuation) of a probe signal by a driven two-level quantum system in the Landau-Zener-St\"uckelberg-Majorana regime by means of an experiment, in which a superconducting qubit was strongly coupled to a microwave cavity, in a conventional arrangement of circuit quantum electrodynamics. Two different types of flux qubit, specifically a conventional Josephson junctions qubit and a phase-slip qubit, show similar results, namely, lasing at the working points where amplification takes place. The experimental data are explained by the interaction of the probe signal with Rabi-like oscillations. The latter are created by constructive interference of Landau-Zener-St\"uckelberg-Majorana (LZSM) transitions during the driving period of the qubit. A detailed description of the occurrence of these oscillations and a comparison of obtained data with both analytic and numerical calculations are given.