Multiphoton antiresonance

We show that nonlinear response of a quantum oscillator displays antiresonant dips and resonant peaks with varying frequency of the driving field. The effect is a consequence of special symmetry and is related to resonant multiphoton mixing of several pairs of oscillator states at a time. We discuss the possibility to observe the antiresonance and the associated multiphoton Rabi oscillations in Josephson junctions.Comment: 4 pages, 3 figures; corrected referenc

Resonant symmetry lifting in a parametrically modulated oscillator

We study a parametrically modulated oscillator that has two stable states of vibrations at half the modulation frequency $\omega_F$. Fluctuations of the oscillator lead to interstate switching. A comparatively weak additional field can strongly affect the switching rates, because it changes the switching activation energies. The change is linear in the field amplitude. When the additional field frequency $\omega_d$ is $\omega_F/2$, the field makes the populations of the vibrational states different thus lifting the states symmetry. If $\omega_d$ differs from $\omega_F/2$, the field modulates the state populations at the difference frequency, leading to fluctuation-mediated wave mixing. For an underdamped oscillator, the change of the activation energy displays characteristic resonant peaks as a function of frequency

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

Relaxation of a qubit measured by a driven Duffing oscillator

We investigate the relaxation of a superconducting qubit for the case when its detector, the Josephson bifurcation amplifier, remains latched in one of its two (meta)stable states of forced vibrations. The qubit relaxation rates are different in different states. They can display strong dependence on the qubit frequency and resonant enhancement, which is due to quasienergy resonances. Coupling to the driven oscillator changes the effective temperature of the qubit.Comment: To appear in Phys. Rev. A (2010

Multiphoton antiresonance in large-spin systems

We study nonlinear response of a spin $S>1/2$ with easy-axis anisotropy. The response displays sharp dips or peaks when the modulation frequency is adiabatically swept through multiphoton resonance. The effect is a consequence of a special symmetry of the spin dynamics in a magnetic field for the anisotropy energy $\propto S_z^2$. The occurrence of the dips or peaks is determined by the spin state. Their shape strongly depends on the modulation amplitude. Higher-order anisotropy breaks the symmetry, leading to sharp steps in the response as function of frequency. The results bear on the dynamics of molecular magnets in a static magnetic field.Comment: Submitted to PR

Quantum interference in the classically forbidden region: a parametric oscillator

We study tunneling between period two states of a parametrically modulated oscillator. The tunneling matrix element is shown to oscillate with the varying frequency of the modulating field. The effect is due to spatial oscillations of the wave function and the related interference in the classically forbidden region. The oscillations emerge already in the ground state of the oscillator Hamiltonian in the rotating frame, which is quartic in the momentum.Comment: Submitted to PR

Pathways of activated escape in periodically modulated systems

We investigate dynamics of activated escape in periodically modulated systems. The trajectories followed in escape form diffusion broadened tubes, which are periodically repeated in time. We show that these tubes can be directly observed and find their shape. Quantitatively, the tubes are characterized by the distribution of trajectories that, after escape, pass through a given point in phase space for a given modulation phase. This distribution may display several peaks separated by the modulation period. Analytical results agree with the results of simulations of a model Brownian particle in a modulated potential

Scaling in activated escape of underdamped systems

Noise-induced escape from a metastable state of a dynamical system is studied close to a saddle-node bifurcation point, but in the region where the system remains underdamped. The activation energy of escape scales as a power of the distance to the bifurcation point. We find two types of scaling and the corresponding critical exponents.Comment: 9 page

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

Laser-like Instabilities in Quantum Nano-electromechanical Systems

We discuss negative damping regimes in quantum nano-electromechanical systems formed by coupling a mechanical oscillator to a single-electron transistor (normal or superconducting). Using an analogy to a laser with a tunable atom-field coupling, we demonstrate how these effects scale with system parameters. We also discuss the fluctuation physics of both the oscillator and the single-electron transistor in this regime, and the degree to which the oscillator motion is coherent.Comment: 4+ pages, 1 figure; reference to the work of Dykman and Krivoglaz adde