Exponential peak and scaling of work fluctuations in modulated systems

We extend the stationary-state work fluctuation theorem to periodically modulated nonlinear systems. Such systems often have coexisting stable periodic states. We show that work fluctuations sharply increase near a kinetic phase transition where the state populations are close to each other. The work variance is proportional here to the reciprocal rate of interstate switching. We also show that the variance displays scaling with the distance to a bifurcation point and find the critical exponent for a saddle-node bifurcation

Strong many-particle localization and quantum computing with perpetually coupled qubits

We demonstrate the onset of strong on-site localization in a one-dimensional many-particle system. The localization is obtained by constructing, in an explicit form, a bounded sequence of on-site energies that eliminates resonant hopping between both nearest and remote sites. This sequence leads to quasi-exponential decay of the single-particle transition amplitude. It also leads to strong localization of stationary many-particle states in a finite-length chain. For an {\it infinite} chain, we instead study the time during which {\it all} many-particle states remain strongly localized. We show that, for any number of particles, this time exceeds the reciprocal frequency of nearest-neighbor hopping by a factor $\sim 10^5$ already for a moderate bandwidth of on-site energies. The proposed energy sequence is robust with respect to small errors. The formulation applies to fermions as well as perpetually coupled qubits. The results show viability of quantum computing with time-independent qubit coupling.Comment: 20 pages, 10 figure

Cooling and squeezing via quadratic optomechanical coupling

We explore the physics of optomechanical systems in which an optical cavity mode is coupled parametrically to the square of the position of a mechanical oscillator. We derive an effective master equation describing two-phonon cooling of the mechanical oscillator. We show that for high temperatures and weak coupling, the steady-state phonon number distribution is non-thermal (Gaussian) and that even for strong cooling the mean phonon number remains finite. Moreover, we demonstrate how to achieve mechanical squeezing by driving the cavity with two beams. Finally, we calculate the optical output and squeezing spectra. Implications for optomechanics experiments with the membrane-in-the-middle geometry or ultracold atoms in optical resonators are discussed.Comment: 4 pages, 3 figure

Quasienergy description of the driven Jaynes-Cummings model

We analyze the driven resonantly coupled Jaynes-Cummings model in terms of a quasienergy approach by switching to a frame rotating with the external modulation frequency and by using the dressed atom picture. A quasienergy surface in phase space emerges whose level spacing is governed by a rescaled effective Planck constant. Moreover, the well-known multiphoton transitions can be reinterpreted as resonant tunneling transitions from the local maximum of the quasienergy surface. Most importantly, the driving defines a quasienergy well which is nonperturbative in nature. The quantum mechanical quasienergy state localized at its bottom is squeezed. In the Purcell limited regime, the potential well is metastable and the effective local temperature close to its minimum is uniquely determined by the squeezing factor. The activation occurs in this case via dressed spin flip transitions rather than via quantum activation as in other driven nonlinear quantum systems such as the quantum Duffing oscillator. The local maximum is in general stable. However, in presence of resonant coherent or dissipative tunneling transitions the system can escape from it and a stationary state arises as a statistical mixture of quasienergy states being localized in the two basins of attraction. This gives rise to a resonant or an antiresonant nonlinear response of the cavity at multiphoton transitions. The model finds direct application in recent experiments with a driven superconducting circuit QED setup.Comment: 13 pages, 8 fi

Dynamical multistability in high-finesse micromechanical optical cavities

We analyze the nonlinear dynamics of a high-finesse optical cavity in which one mirror is mounted on a flexible mechanical element. We find that this system is governed by an array of dynamical attractors, which arise from phase-locking between the mechanical oscillations of the mirror and the ringing of the light intensity in the cavity. We describe an analytical approximation to map out the diagram of attractors in parameter space, derive the slow amplitude dynamics of the system, including thermally activated hopping between different attractors, and suggest a scheme for exploiting the dynamical multistability in the measurement of small displacements.Comment: 5 pages, 4 figure

Theory of Second and Higher Order Stochastic Processes

This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial example is $\ddot x = R(t)$, where $R(t)$ is not a Gaussian white noise). The stochastic process is discretized into $n$ time-steps, all possible realizations are summed up and the continuum limit is taken. This procedure often yields closed form formulas for the joint probability distributions. Completely worked out examples include all Gaussian random forces and a large class of Markovian (non-Gaussian) forces. This approach is also useful for deriving Fokker-Planck equations for the probability distribution functions. This is worked out for Gaussian noises and for the Markovian dichotomous noise.Comment: 35 pages, PlainTex, accepted for publication in Phys Rev. E

On-chip cavity quantum phonodynamics with an acceptor qubit in silicon

We describe a chip-based, solid-state analogue of cavity-QED utilizing acoustic phonons instead of photons. We show how long-lived and tunable acceptor impurity states in silicon nanomechanical cavities can play the role of a matter non-linearity for coherent phonons just as, e.g., the Josephson qubit plays in circuit-QED. Both strong coupling (number of Rabi oscillations ~ 100) and strong dispersive coupling (0.1-2 MHz) regimes can be reached in cavities in the 1-20 GHz range, enabling the control of single phonons, phonon-phonon interactions, dispersive phonon readout of the acceptor qubit, and compatibility with other optomechanical components such as phonon-photon translators. We predict explicit experimental signatures of the acceptor-cavity system.Comment: 6 pages, 2 figures, PDFLaTeX. New version improves clarit

Flux reversal in a two-state symmetric optical thermal ratchet

A Brownian particle's random motions can be rectified by a periodic potential energy landscape that alternates between two states, even if both states are spatially symmetric. If the two states differ only by a discrete translation, the direction of the ratchet-driven current can be reversed by changing their relative durations. We experimentally demonstrate flux reversal in a symmetric two-state ratchet by tracking the motions of colloidal spheres moving through large arrays of discrete potential energy wells created with dynamic holographic optical tweezers. The model's simplicity and high degree of symmetry suggest possible applications in molecular-scale motors.Comment: 4 pages, 5 figures, accepted for publication in Physical Review E, Rapid Communication

Scalable design of tailored soft pulses for coherent control

We present a scalable scheme to design optimized soft pulses and pulse sequences for coherent control of interacting quantum many-body systems. The scheme is based on the cluster expansion and the time dependent perturbation theory implemented numerically. This approach offers a dramatic advantage in numerical efficiency, and it is also more convenient than the commonly used Magnus expansion, especially when dealing with higher order terms. We illustrate the scheme by designing 2nd-order pi-pulses and a 6th-order 8-pulse refocusing sequence for a chain of qubits with nearest-neighbor couplings. We also discuss the performance of soft-pulse refocusing sequences in suppressing decoherence due to low-frequency environment.Comment: 4 pages, 2 tables. (modified first table, references added, minor text changes

Noise-Induced Linearisation and Delinearisation

It is demonstrated, by means of analogue electronic simulation and theoretically, that external noise can markedly change the character of the response of a nonlinear system to a low-frequency periodic field. In general, noise of sufficient intensity {\it linearises} the response. For certain parameter ranges in particular cases, however, an increase in the noise intensity can sometime have the opposite effect and is shown to {\it delinearise} the response. The physical origins of these contrary behaviours are discussed.Comment: 17 pages. No special macros. Figures on reques