20 research outputs found
Parametric resonance in tunable superconducting cavities
We develop a theory of parametric resonance in tunable superconducting
cavities. The nonlinearity introduced by the SQUID attached to the cavity, and
damping due to connection of the cavity to a transmission line are taken into
consideration. We study in detail the nonlinear classical dynamics of the
cavity field below and above the parametric threshold for the degenerate
parametric resonance, featuring regimes of multistability and parametric
radiation. We investigate the phase-sensitive amplification of external signals
on resonance, as well as amplification of detuned signals, and relate the
amplifier performance to that of linear parametric amplifiers. We also discuss
applications of the device for dispersive qubit readout. Beyond the classical
response of the cavity, we investigate small quantum fluctuations around the
amplified classical signals. We evaluate the noise power spectrum both for the
internal field in the cavity and the output field. Other quantum statistical
properties of the noise are addressed such as squeezing spectra, second order
coherence, and two-mode entanglement.Comment: 25 pages, 17 figure
Parametric Effects in Circuit Quantum Electrodynamics (Review Article)
We review recent advances in the research on quantum parametric phenomena in superconducting circuits with Josephson junctions. We discuss physical processes in parametrically driven tunable cavity and outline theoretical foundations for their description. Amplification and frequency conversion are discussed in detail for degenerate and non-degenerate parametric resonance, including quantum noise squeezing and photon entanglement. Experimental advances in this area played decisive role in successful development of quantum limited parametric amplifiers for superconducting quantum information technology. We also discuss nonlinear down-conversion processes and experiments on self-sustained parametric and subharmonic oscillations
Generalized Bose-Einstein condensation into multiple states in driven-dissipative systems
Bose-Einstein condensation, the macroscopic occupation of a single quantum
state, appears in equilibrium quantum statistical mechanics and persists also
in the hydrodynamic regime close to equilibrium. Here we show that even when a
degenerate Bose gas is driven into a steady state far from equilibrium, where
the notion of a single-particle ground state becomes meaningless, Bose-Einstein
condensation survives in a generalized form: the unambiguous selection of an
odd number of states acquiring large occupations. Within mean-field theory we
derive a criterion for when a single and when multiple states are Bose selected
in a non-interacting gas. We study the effect in several driven-dissipative
model systems, and propose a quantum switch for heat conductivity based on
shifting between one and three selected states.Comment: 5+3 pages, 2+2 figure
Non-equilibrium steady states of ideal bosonic and fermionic quantum gases
We investigate non-equilibrium steady states of driven-dissipative ideal
quantum gases of both bosons and fermions. We focus on systems of sharp
particle number that are driven out of equilibrium either by the coupling to
several heat baths of different temperature or by time-periodic driving in
combination with the coupling to a heat bath. Within the framework of
(Floquet-)Born-Markov theory, several analytical and numerical methods are
described in detail. This includes a mean-field theory in terms of occupation
numbers, an augmented mean-field theory taking into account also non-trivial
two-particle correlations, and quantum-jump-type Monte-Carlo simulations. For
the case of the ideal Fermi gas, these methods are applied to simple lattice
models and the possibility of achieving exotic states via bath engineering is
pointed out. The largest part of this work is devoted to bosonic quantum gases
and the phenomenon of Bose selection, a non-equilibrium generalization of Bose
condensation, where multiple single-particle states are selected to acquire a
large occupation [Phys. Rev. Lett. 111, 240405 (2013)]. In this context, among
others, we provide a theory for transitions where the set of selected states
changes, describe an efficient algorithm for finding the set of selected
states, investigate beyond-mean-field effects, and identify the dominant
mechanisms for heat transport in the Bose selected state
Switching mechanism in periodically driven quantum systems with dissipation
We introduce a switching mechanism in the asymptotic occupations of quantum
states induced by the combined effects of a periodic driving and a weak
coupling to a heat bath. It exploits one of the ubiquitous avoided crossings in
driven systems and works even if both involved Floquet states have small
occupations. It is independent of the initial state and the duration of the
driving. As a specific example of this general switching mechanism we show how
an asymmetric double well potential can be switched between the lower and the
upper well by a periodic driving that is much weaker than the asymmetry.Comment: 5 pages, 5 figure
Nondegenerate Parametric Resonance in a Tunable Superconducting Cavity
We develop a theory for nondegenerate parametric resonance in a tunable superconducting cavity. We focus on nonlinear effects that are caused by nonlinear Josephson elements connected to the cavity. We analyze parametric amplification in a strong nonlinear regime at the parametric-instability threshold, and we calculate maximum gain values. Above the threshold, in the parametric-oscillator regime, the cavity linear response diverges at the oscillator frequency at all pump strengths. We show that this divergence is related to the continuous degeneracy of the free oscillator state with respect to the phase. Applying on-resonance input lifts the degeneracy and removes the divergence. We also investigate quantum noise squeezing. It is shown that in the strong amplification regime, the noise undergoes four-mode squeezing, and that, in this regime, the output signal-to-noise ratio can significantly exceed the input value. We also analyze the intermode frequency conversion and identify the parameters at which full conversion is achieved
Statistical mechanics of Floquet systems with regular and chaotic states
We investigate the asymptotic state of time-periodic quantum systems with
regular and chaotic Floquet states weakly coupled to a heat bath. The
asymptotic occupation probabilities of these two types of states follow
fundamentally different distributions. Among regular states the probability
decreases from the state in the center of a regular island to the outermost
state by orders of magnitude, while chaotic states have almost equal
probabilities. We derive an analytical expression for the occupations of
regular states of kicked systems, which depends on the winding numbers of the
regular tori and the parameters temperature and driving frequency. For a
constant winding number within a regular island it simplifies to Boltzmann-like
weights \exp(-\betaeff \Ereg_m), similar to time-independent systems. For
this we introduce the regular energies \Ereg_m of the quantizing tori and an
effective winding-number-dependent temperature 1/\betaeff, different from the
actual bath temperature. Furthermore, the occupations of other typical Floquet
states in a mixed phase space are studied, i.e. regular states on nonlinear
resonances, beach states, and hierarchical states, giving rise to distinct
features in the occupation distribution. Avoided crossings involving a regular
state lead to drastic consequences for the entire set of occupations. We
introduce a simplified rate model whose analytical solutions describe the
occupations quite accurately.Comment: 18 pages, 11 figure