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

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

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

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

Diffusion-induced dephasing in nanomechanical resonators

We study resonant response of an underdamped nanomechanical resonator with fluctuating frequency. The fluctuations are due to diffusion of molecules or microparticles along the resonator. They lead to broadening and change of shape of the oscillator spectrum. The spectrum is found for the diffusion confined to a small part of the resonator and where it occurs along the whole nanobeam. The analysis is based on extending to the continuous limit, and appropriately modifying, the method of interfering partial spectra. We establish the conditions of applicability of the fluctuation-dissipation relations between the susceptibility and the power spectrum. We also find where the effect of frequency fluctuations can be described by a convolution of the spectra without these fluctuations and with them as the only source of the spectral broadening.Comment: 10 page

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

Many-particle confinement by constructed disorder and quantum computing

Many-particle confinement (localization) is studied for a 1D system of spinless fermions with nearest-neighbor hopping and interaction, or equivalently, for an anisotropic Heisenberg spin-1/2 chain. This system is frequently used to model quantum computers with perpetually coupled qubits. We construct a bounded sequence of site energies that leads to strong single-particle confinement of all states on individual sites. We show that this sequence also leads to a confinement of all many-particle states in an infinite system for a time that scales as a high power of the reciprocal hopping integral. The confinement is achieved for strong interaction between the particles while keeping the overall bandwidth of site energies comparatively small. The results show viability of quantum computing with time-independent qubit coupling.Comment: An invited paper for the topical issue of J. Opt. B on quantum contro

Antiresonance and interaction-induced localization in spin and qubit chains with defects

We study a spin chain with an anisotropic XXZ coupling in an external field. Such a chain models several proposed types of a quantum computer. The chain contains a defect with a different on-site energy. The interaction between excitations is shown to lead to two-excitation states localized next to the defect. In a resonant situation scattering of excitations on each other might cause decay of an excitation localized on the defect. We find that destructive quantum interference suppresses this decay. Numerical results confirm the analytical predictions.Comment: Updated versio

Diffusion-induced bistability of driven nanomechanical resonators

We study nanomechanical resonators with frequency fluctuations due to diffusion of absorbed particles. The diffusion depends on the vibration amplitude through inertial effect. We find that, if the diffusion coefficient is sufficiently large, the resonator response to periodic driving displays bistability. The lifetime of the coexisting vibrational states scales exponentially with the diffusion coefficient. It also displays a characteristic scaling dependence on the distance to bifurcation points.Comment: 4 pages, 3 figure