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arXiv:0802.0304 · Physical Review Letters

Photon-Number Squeezing in Circuit Quantum Electrodynamics

Michael Marthaler, Gerd Schön, Alexander Shnirman

Published Sep 29, 2008• 31 citations
arXivHTMLPDF

Abstract

A superconducting single-electron transistor (SSET) coupled to an anharmonic oscillator, e.g., a Josephson junction-L-C circuit, can drive the latter to a nonequilibrium photon-number distribution. By biasing the SSET at the Josephson quasiparticle cycle, cooling of the oscillator as well as a laserlike enhancement of the photon number can be achieved. Here, we show that the cutoff in the quasiparticle tunneling rate due to the superconducting gap, in combination with the anharmonicity of the oscillator, may create strongly squeezed photon-number distributions. For low dissipation in the oscillator, nearly pure Fock states can be produced.

DOI
10.1103/physrevlett.101.147001

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A superconducting single-electron transistor (SSET) coupled to an anharmonic oscillator, e.g., a Josephson junction-L-C circuit, can drive the latter to a nonequilibrium photon-number distribution. By biasing the SSET at the Josephson quasiparticle cycle, cooling of the oscillator as well as a laserlike enhancement of the photon number can be achieved. Here, we show that the cutoff in the quasiparticle tunneling rate due to the superconducting gap, in combination with the anharmonicity of the oscillator, may create strongly squeezed photon-number distributions. For low dissipation in the oscillator, nearly pure Fock states can be produced.
We study a superconducting single-electron transistor (SSET) which is coupled to a LC\mathit{LC}LC oscillator via the phase difference across one of the Josephson junctions. This leads to a strongly anharmonic coupling between the SSET and the oscillator. The coupling can oscillate with the number of photons, which makes this system very similar to the single-atom injection maser. However, the advantage of a design based on superconducting circuits is the strong coupling and existence of standard methods to measure the radiation field in the oscillator. This makes it possible to study many effects that have been predicted for the single-atom injection maser in a circuit quantum electrodynamics setup.
In circuit quantum electrodynamical systems, the quasiparticle-related losses in Josephson junctions are suppressed due to the gap in the superconducting density of states which is much higher than the typical energy of a microwave photon. In this work, we show that a strong drive even at a frequency lower than twice the superconductor gap parameter can activate dissipation in the junctions due to photon-assisted breaking of the Cooper pairs. Both the decay rate and noise strength associated with the losses are sensitive to the dc phase bias of the junction and can be tuned in a broad range by the amplitude and the frequency of the external driving field, making the suggested mechanism potentially attractive for designing tunable dissipative elements. We also predict pronounced memory effects in the driven Josephson junctions, which are appealing for both theoretical and experimental studies of non-Markovian physics in superconducting quantum circuits. We illustrate our theoretical findings by studying the spectral properties and the steady-state population of a low-impedance resonator coupled to the driven Josephson junction: we show the emergence of non-Lorentzian spectral lines and broad tunability of effective temperature of the steady state.
The Josephson quasiparticle (JQP) cycle in a voltage-biased superconducting single-electron transistor (SSET) combines coherent Cooper pair tunneling with incoherent quasiparticle decay. We have measured the influence of current flow through an independently-biased SSET on the JQP cycle when the two SSET's have a strong mutual capacitive coupling. We find, among other effects, that the JQP current in one SSET is enhanced by the presence of a quasiparticle current in the other SSET. A simplified model of the coupled-SSET system is presented which reproduces the enhancement effect.
We analyze the quantum dynamics of two electromagnetic oscillators coupled in series to a voltage-biased Josephson junction. When the applied voltage leads to a Josephson frequency across the junction which matches the sum of the two mode frequencies, tunneling Cooper pairs excite photons in both modes simultaneously leading to far-from-equilibrium states. These states display highly nonclassical features including strong antibunching, violation of Cauchy-Schwartz inequalities, and number squeezing. We obtain approximate analytic results for both the regimes of low and high photon occupancies which are supported by a full numerical treatment. The impact of asymmetries between the two modes is explored, revealing a pronounced enhancement of number squeezing when the modes are damped at different rates.
A superconducting qubit in the strong dispersive regime of circuit quantum electrodynamics is a powerful probe for microwave photons in a cavity mode. In this regime, a qubit excitation spectrum is split into multiple peaks, with each peak corresponding to an individual photon number in the cavity (discrete ac Stark shift). Here, we measure the qubit spectrum in a cavity that is driven continuously with a squeezed vacuum generated by a Josephson parametric amplifier. By fitting the obtained spectrum with a model which takes into account the finite qubit excitation power, we determine the photon number distribution, which reveals an even-odd photon number oscillation and quantitatively fulfills Klyshko's criterion for nonclassicality.
Superconducting qubits coupled to electric or nanomechanical resonators display effects previously studied in quantum electrodynamics (QED) as well as extensions thereof. Here, we consider a driven qubit coupled to a low-frequency oscillator and study the influence of dissipation. When the qubit is driven to perform Rabi oscillations, with Rabi frequency in resonance with the oscillator, the latter can be driven far from equilibrium. Blue detuned driving leads to a population inversion in the qubit and lasing behavior of the oscillator ('single-atom laser'). For red detuning, the qubit cools the oscillator. This behavior persists at the symmetry point where the qubit–oscillator coupling is quadratic and decoherence effects are minimized. Here, the system realizes a 'single-atom-two-photon laser'.