Efficient on-chip source of microwave photon pairs in superconducting circuit QED

We describe a scheme for the efficient generation of microwave photon pairs by parametric downconversion in a superconducting transmission line resonator coupled to a Cooper pair box serving as an artificial atom. By properly tuning the first three levels with respect to the cavity modes, the down-conversion probability may become higher than in the most efficient schemes for optical photons. We show this by numerically simulating the dissipative quantum dynamics of the coupled cavity-box system and discuss the effects of dephasing and relaxation. The setup analyzed here might form the basis for a future on-chip source of entangled microwave photons.Comment: 5 pages, 5 figure

Thermalization of Interacting Fermions and Delocalization in Fock space

By means of exact diagonalization, we investigate the onset of 'eigenstate thermalization' and the crossover to ergodicity in a system of 1D fermions with increasing interaction. We show that the fluctuations in the expectation values of the momentum distribution from eigenstate to eigenstate decrease with increasing coupling strength and system size. It turns out that these fluctuations are proportional to the inverse participation ratio of eigenstates represented in the Fock basis. We demonstrate that eigenstate thermalization should set in even for vanishingly small perturbations in the thermodynamic limit.Comment: 4 pages, 4 figure

Single-site-resolved measurement of the current statistics in optical lattices

At present, great effort is spent on the experimental realization of gauge fields for quantum many-body systems in optical lattices. At the same time, the single-site-resolved detection of individual atoms has become a new powerful experimental tool. We discuss a protocol for the single-site resolved measurement of the current statistics of quantum many-body systems, which makes use of a bichromatic optical superlattice and single-site detection. We illustrate the protocol by a numerical study of the current statistics for interacting bosons in one and two dimensions and discuss the role of the on-site interactions for the current pattern and the ground-state symmetry for small two-dimensional lattices with artificial magnetic fields.Comment: 5+2 pages, published versio

Quantum Measurement of Phonon Shot Noise

We provide a full quantum mechanical analysis of a weak energy measurement of a driven mechanical resonator. We demonstrate that measurements too weak to resolve individual mechanical Fock states can nonetheless be used to unambiguously detect the non-classical energy fluctuations of the driven mechanical resonator, i.e. "phonon shot noise". We also show that the third moment of the oscillator's energy fluctuations provides a far more sensitive probe of quantum effects than the second moment, and that measuring the third moment via the phase shift of light in an optomechanical setup directly yields the type of operator ordering postulated in the theory of full-counting statistics.Comment: 4 pages, 1 figur

Noise-Induced Transitions in Optomechanical Synchronization

We study how quantum and thermal noise affects synchronization of two optomechanical limit-cycle oscillators. Classically, in the absence of noise, optomechanical systems tend to synchronize either in-phase or anti-phase. Taking into account the fundamental quantum noise, we find a regime where fluctuations drive transitions between these classical synchronization states. We investigate how this "mixed" synchronization regime emerges from the noiseless system by studying the classical-to-quantum crossover and we show how the time scales of the transitions vary with the effective noise strength. In addition, we compare the effects of thermal noise to the effects of quantum noise

Quantum-coherent phase oscillations in synchronization

Recently, several studies have investigated synchronization in quantum-mechanical limit-cycle oscillators. However, the quantum nature of these systems remained partially hidden, since the dynamics of the oscillator's phase was overdamped and therefore incoherent. We show that there exist regimes of underdamped and even quantum-coherent phase motion, opening up new possibilities to study quantum synchronization dynamics. To this end, we investigate the Van der Pol oscillator (a paradigm for a self-oscillating system) synchronized to an external drive. We derive an effective quantum model which fully describes the regime of underdamped phase motion and additionally allows us to identify the quality of quantum coherence. Finally, we identify quantum limit cycles of the phase itself.Comment: 6 pages + Supplemental Materia

Perturbative corrections to the Gutzwiller mean-field solution of the Mott-Hubbard model

We study the Mott-insulator transition of bosonic atoms in optical lattices. Using perturbation theory, we analyze the deviations from the mean-field Gutzwiller ansatz, which become appreciable for intermediate values of the ratio between hopping amplitude and interaction energy. We discuss corrections to number fluctuations, order parameter, and compressibility. In particular, we improve the description of the short-range correlations in the one-particle density matrix. These corrections are important for experimentally observed expansion patterns, both for bulk lattices and in a confining trap potential.Comment: 10 pages, 10 figue

Localized phase structures growing out of quantum fluctuations in a quench of tunnel-coupled atomic condensates

We investigate the relative phase between two weakly interacting 1D condensates of bosonic atoms after suddenly switching on the tunnel-coupling. The following phase dynamics is governed by the quantum sine-Gordon equation. In the semiclassical limit of weak interactions, we observe the parametric amplification of quantum fluctuations leading to the formation of breathers with a finite lifetime. The typical lifetime and density of the these 'quasibreathers' are derived employing exact solutions of the classical sine-Gordon equation. Both depend on the initial relative phase between the condensates, which is considered as a tunable parameter.Comment: 7 pages, 5 figure

From Kardar-Parisi-Zhang scaling to explosive desynchronization in arrays of limit-cycle oscillators

We study the synchronization physics of 1D and 2D oscillator lattices subject to noise and predict a dynamical transition that leads to a sudden drastic increase of phase diffusion. Our analysis is based on the widely applicable Kuramoto-Sakaguchi model, with local couplings between oscillators. For smooth phase fields, the time evolution can initially be described by a surface growth model, the Kardar-Parisi-Zhang (KPZ) theory. We delineate the regime in which one can indeed observe the universal KPZ scaling in 1D lattices. For larger couplings, both in 1D and 2D, we observe a stochastic dynamical instability that is linked to an apparent finite-time singularity in a related KPZ lattice model. This has direct consequences for the frequency stability of coupled oscillator lattices, and it precludes the observation of non-Gaussian KPZ-scaling in 2D lattices.Comment: 9 pages, 5 figure