arXiv subjects

M. I. Dykman

Publications and source records attributed to M. I. Dykman.

At least 91 records · Page 5Linked to original sources

arXiv2007

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.

cond-mat.mes-hall↗

arXiv2007

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.

cond-mat.mes-hall↗

arXiv2006

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 $ω_F$. 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 $ω_d$ is $ω_F/2$, the field makes the populations of the vibrational states different thus lifting the states symmetry. If $ω_d$ differs from $ω_F/2$, 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.

cond-mat.stat-mech↗

arXiv2006

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.

cond-mat.stat-mech↗

arXiv2006

Critical exponents in metastable decay via quantum activation

We consider decay of metastable states of forced vibrations of a quantum oscillator close to bifurcation points, where dissipation becomes effectively strong. We show that decay occurs via quantum activation over an effective barrier. The decay probability $W$ scales with the distance $η$ to the bifurcation point as $|\ln W|\propto η^ξ$. The exponent $ξ$ is found for a resonantly driven oscillator and an oscillator modulated at nearly twice its eigenfrequency.

cond-mat.mes-hall↗

arXiv2005

Fault-Tolerant Landau-Zener Quantum Gates

We present a method to perform fault-tolerant single-qubit gate operations using Landau-Zener tunneling. In a single Landau-Zener pulse, the qubit transition frequency is varied in time so that it passes through the frequency of the radiation field. We show that a simple three-pulse sequence allows eliminating errors in the gate up to the third order in errors in the qubit energies or the radiation frequency.

quant-ph↗

arXiv2005

Multiphoton Antiresonance and Quantum Activation in Driven Systems

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 also discuss escape from a metastable state of forced vibrations. Two important examples show that the probability of escape via diffusion over quasienergy is larger than via dynamical tunneling provided the relaxation rate exceeds both of them. Diffusion dominates even for zero temperature, so that escape occurs via quantum rather than thermal activation. The effects can be studied using Josephson junctions and Josephson-junction based systems.

quant-ph↗

arXiv2005

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.

cond-mat.mes-hall↗

arXiv2005

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.

cond-mat.mes-hall↗

arXiv2005

Activated escape of periodically modulated systems

The rate of noise-induced escape from a metastable state of a periodically modulated overdamped system is found for an arbitrary modulation amplitude $A$. The instantaneous escape rate displays peaks that vary with the modulation from Gaussian to strongly asymmetric. The prefactor $ν$ in the period-averaged escape rate depends on $A$ nonmonotonically. Near the bifurcation amplitude $A_c$ it scales as $ν\propto (A_c-A)^ζ$. We identify three scaling regimes, with $ζ= 1/4, -1$, and 1/2.

cond-mat.mes-hall↗

arXiv2004

Multiphoton antiresonance

cond-mat.mes-hall↗

arXiv2004

Many-particle localization by constructed disorder: enabling quantum computing with perpetually coupled qubits

We demonstrate that, in a many-particle system, particles can be strongly confined to their sites. The localization is obtained by constructing a sequence of on-site energies that efficiently suppresses resonant hopping. The time during which a many-particle state remains strongly localized in an infinite chain can exceed the reciprocal hopping frequency by $\agt 10^6$ already for a narrow energy bandwidth. The results show viability of quantum computers with time-independent qubit coupling.

cond-mat.mes-hall↗

arXiv2004

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.

quant-ph↗

arXiv2003

Scaling and crossovers in activated escape near a bifurcation point

Near a bifurcation point a system experiences critical slowing down. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node bifurcation where a metastable state disappears. The rate of activated escape $W$ scales with the driving field amplitude $A$ as $\ln W \propto (A_c-A)^ξ$, where $A_c$ is the bifurcational value of $A$. With increasing field frequency the critical exponent $ξ$ changes from $ξ= 3/2$ for stationary systems to a dynamical value $ξ=2$ and then again to $ξ=3/2$. The analytical results are in agreement with the results of asymptotic calculations in the scaling region. Numerical calculations and simulations for a model system support the theory.

cond-mat.mes-hall↗

arXiv2003

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.

cond-mat↗

arXiv2003

Two-particle localization and antiresonance in disordered spin and qubit chains

We show that, in a system with defects, two-particle states may experience destructive quantum interference, or antiresonance. It prevents an excitation localized on a defect from decaying even where the decay is allowed by energy conservation. The system studied is a qubit chain or an equivalent spin chain with an anisotropic ($XXZ$) exchange coupling in a magnetic field. The chain has a defect with an excess on-site energy. It corresponds to a qubit with the level spacing different from other qubits. We show that, because of the interaction between excitations, a single defect may lead to multiple localized states. The energy spectra and localization lengths are found for two-excitation states. The localization of excitations facilitates the operation of a quantum computer. Analytical results for strongly anisotropic coupling are confirmed by numerical studies.

quant-ph↗

arXiv2003

Acceptor-based silicon quantum computing

A solid-state quantum computer with dipolar coupling between qubits is proposed. The qubits are formed by the low-lying states of an isolated acceptor in silicon. The system has the scalability inherent to spin-based solid state systems, but the spatial separation between the qubits is an order of magnitude larger. Despite strong dipolar inter-qubit coupling, the decoherence rate, as measured by electric dipolar echoes at an energy splitting of 1.5 GHz, is less than 1 kHz at low temperatures. For inter-acceptor distances of 100 nm and for modest microwave field amplitudes (50 V/cm) the clock frequency of the quantum computer is 0.1 GHz, which yields a quality factor of 105. This paper describes ideas for detection and operation of the quantum computer, and examines limitations imposed by noise sources.

cond-mat.mes-hall↗

arXiv2003

Electron Dynamics in Quantum Dots on Helium Surface

We study single-electron quantum dots on helium surface created by electrodes submerged into the helium. The intradot potential is electrostatically controlled. We find the electron energy spectrum and identify relaxation mechanisms. Strong in-plane confinement significantly slows down electron relaxation. Energy relaxation is due primarily to coupling to phonons in helium. Dephasing is determined by thermally excited ripplons and by noise from underlying electrodes. The decay rate can be further suppressed by a magnetic field normal to the helium surface. Slow relaxation in combination with control over the energy spectrum make localized electrons appealing as potential qubits of a quantum computer.

cond-mat↗