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Alexandre M. Zagoskin

Publications and source records attributed to Alexandre M. Zagoskin.

14 recordsLinked to original sources
arXiv2018

Pechukas-Yukawa formalism for Landau-Zener transitions in the presence of external noise

Quantum systems are prone to decoherence due to both intrinsic interactions as well as random fluctuations from the environment. Using the Pechukas-Yukawa formalism, we investigate the influence of noise on the dynamics of an adiabatically evolving Hamiltonian which can describe a quantum computer. Under this description, the level dynamics of a parametrically perturbed quantum Hamiltonian are mapped to the dynamics of 1D classical gas. We show that our framework coincides with the results of the classical Landau-Zener transitions upon linearisation. Furthermore, we determine the effects of external noise on the level dynamics and its impact on Landau-Zener transitions.

cond-mat.stat-mech↗
arXiv2017

BBGKY chain and kinetic equations for the level dynamics in an externally perturbed quantum system

Theoretical description and simulation of large quantum coherent systems out of equilibrium remains a daunting task. Here we are developing a new approach to it based on the Pechukas-Yukawa formalism, which is especially convenient in case of an adiabatically slow external perturbation. In this formalism the dynamics of energy levels in an externally perturbed quantum system as a function of the perturbation parameter is mapped on that of a fictitious one-dimensional classical gas of particles with cubic repulsion. Equilibrium statistical mechanics of this Pechukas gas allows to reproduce the random matrix theory of energy levels. In the present work, we develop the nonequilibrium statistical mechanics of the Pechukas gas, starting with the derivation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) chain of equations for the appropriate generalized distribution functions. Sets of approximate kinetic equations can be consistently obtained by breaking this chain at a particular point (i.e. approximating all higher-order distribution functions by the products of the lower-order ones). When complemented by the equations for the level occupation numbers and inter-level transition amplitudes, they allow to describe the nonequilibrium evolution of the quantum state of the system, which can describe better a large quantum coherent system than the currently used approaches. In particular, we find that corrections to the factorized approximation of the distribution function scale as 1/N, where N is the number of the "Pechukas gas particles" (i.e. energy levels in the system).

cond-mat.stat-mech↗
arXiv2014

State-dependent photon blockade via quantum-reservoir engineering

An arbitrary initial state of an optical or microwave field in a lossy driven nonlinear cavity can be changed, in the steady-state limit, into a partially incoherent superposition of only the vacuum and the single-photon states. This effect is known as single-photon blockade, which is usually analyzed for a Kerr-type nonlinear cavity parametrically driven by a single-photon process assuming single-photon loss mechanisms. We study photon blockade engineering via a squeezed reservoir, i.e., a quantum reservoir, where only two-photon absorption is allowed. Namely, we analyze a lossy nonlinear cavity parametrically driven by a two-photon process and allowing two-photon loss mechanisms, as described by the master equation derived for a two-photon absorbing reservoir. The nonlinear cavity engineering can be realized by a linear cavity with a tunable two-level system via the Jaynes-Cummings interaction in the dispersive limit. We show that by tuning properly the frequencies of the driving field and the two-level system, the steady state of the cavity field can be the single-photon Fock state or a partially incoherent superposition of several Fock states with photon numbers, e.g., (0,2), (1,3), (0,1,2), or (0,2,4). We observe that an arbitrary initial coherent or incoherent superposition of Fock states with an even (odd) number of photons can be changed into a partially incoherent superposition of a few Fock states of the same photon-number parity. A general solution for an arbitrary initial state is a weighted mixture of the above two solutions with even and odd photon numbers, where the weights are given by the probabilities of measuring the even and odd numbers of photons of the initial cavity field, respectively. Thus, in contrast to the standard photon blockade, we prove that the steady state in the engineered photon blockade, can depend on its initial state.

quant-ph↗
arXiv2014

Toroidal qubits: naturally-decoupled quiet artificial atoms

The requirements of quantum computations impose high demands on the level of qubit protection from perturbations; in particular, from those produced by the environment. Here we propose a superconducting flux qubit design that is naturally protected from ambient noise. This decoupling is due to the qubit interacting with the electromagnetic field only through its toroidal moment, which provides an unusual qubit-field interaction.

quant-ph↗
arXiv2008

On "non-Hermitian Quantum Mechanics"

A series of recent papers ``Faster than Hermitian Quantum Mechanics'' and related articles made a point of the possibility of a non-Hermitian, but PT-symmetric, operator to play the role of a Hamiltonian. In particular, they show that with an appropriate choice of an inner product, the evolution generated by such an operator will conserve the norm and scalar product. Here we observe that if one chooses such an inner product then the Hamiltonian in question is actually Hermitian, and the whole exercise is to a certain degree redundant.

quant-ph↗
arXiv2003

Theory of anomalous magnetic interference pattern in mesoscopic SNS Josephson junctions

The magnetic interference pattern in mesoscopic SNS Josephson junctions is sensitive to the scattering in the normal part of the system. In this paper we investigate it, generalizing Ishii's formula for current-phase dependence to the case of normal scattering at NS boundaries in an SNS junction of finite width. The resulting flattening of the first diffraction peak is consistent with experimental data for S-2DEG-S mesoscopic junctions.

cond-mat.supr-con↗
arXiv1999

A scalable, tunable qubit, based on a clean DND or grain boundary D-D junction

Unique properties of a ballistic DND or grain boundary D-D junction, including doubly degenerate ground state with tunable potential barrier between the "up" and "down" states and non-quantized spontaneous magnetic flux, make it a good candidate for a solid state qubit. The role of quantum "spin" variable is played by the sign of equilibrium superconducting phase difference on the junction, which is revealed in the direction of spontaneous supercurrent flow in equilibrium. Possibilities of design-specific simultaneous operations with several integrated qubits are discussed.

cond-mat.supr-con↗
arXiv1999

Voltage fluctuations on a superconductor grain attached to a quantum wire

When a finite superconductor is in contact with a 1D normal conductor, superconducting phase fluctuations lead to power-law response of the normal subsystem. As a result, the charge fluctuations on the superconductor at zero temperature have logarithmic correlator and a 1/ωpower spectrum (1/f-noise). At higher temperatures 1/ωis pushed to the high frequency region, and 1/ω^2 behavior prevails.

cond-mat.supr-con↗
arXiv1998

Coherent transport and nonlocality in mesoscopic SNS junctions: anomalous magnetic interference patterns

We show that in {\em ballistic} mesoscopic SNS junctions the period of critical current vs. magnetic flux dependence (magnetic interference pattern), $I_c(Φ)$, changes {\em continuously and non-monotonically} from $Φ_0$ to $2Φ_0$ as the length-to-width ratio of the junction grows, or temperature drops. In {\em diffusive} mesoscopic junctions the change is even more drastic, with the first zero of $I_c(Φ)$ appearing at $3Φ_0$. The effect is a manifestation of nonlocal relation between the supercurrent density and superfluid velocity in the normal part of the system, with the characteristic scale $ξ_T = \hbar v_F/2πk_BT$ (ballistic limit) or $\tildeξ_T = \sqrt{\hbar D/2πk_BT}$ (diffusive limit), the normal metal coherence length, and arises due to restriction of the quasiparticle phase space near the lateral boundaries of the junction. It explains the $2Φ_0$-periodicity recently observed by Heida et al. (Phys. Rev. B {\bf 57}, R5618 (1998)). We obtained explicit analytical expressions for the magnetic interference pattern for a junction with an arbitrary length-to-width ratio. Experiments are proposed to directly observe the $Φ_0\to 2Φ_0$- and $Φ_0\to 3Φ_0$-transitions.

cond-mat.supr-con↗
arXiv1998

Driving-voltage-induced mechanical force oscillations in metal quantum point contacts

We predict that the mesoscopic tensile force fluctuations in metal quantum point contacts (nanowires) arise as a result of finite electric voltage on the contact. They are due to reconfiguration of the electronic subsystem and are correlated with the nonlinearities of the current-voltage characteristics of the contact. The observation of the effect would directly confirm the recently suggested "free-electron" mechanism of mesoscopic force fluctuations observed in nanowires under deformation. The related magnetic susceptibility fluctuations and role of topology of the wire cross section are discussed as well

cond-mat.mes-hall↗
arXiv1997

Half-Periodic Josephson Effect in an s-Wave Superconductor - Normal Metal -d-Wave Superconductor Junction

We predict that the Josephson current in a clean s-wave superconductor-normal metal-d-wave superconductor junction is periodic in superconducting phase difference $ϕ$ with period $π$ instead of $2π$. The frequency of non-stationary Josephson effect is correspondingly $2ω_J = 4eV.$ The effect is due to coexistence in the normal layer of current carrying Andreev levels with phase differences $ϕ$ and $ϕ+π.$

cond-mat.supr-con↗
arXiv1997

Fermi Edge Singularities: Boundstates and Finite Size Effects

Fermi edge adsorption singularities (FES) are studied using a combination of conformal field theory (CFT), an exact sum rule and numerical work on a tight binding model which is shown to exhibit remarkable simplifying features. The relationship between FES and Anderson orthogonality exponent is established in great generality, using CFT, including the case where the core hole potential produces a boundstate. Universal results on the adsorption intensity in a finite sized sample are obtained. Various predictions are checked numerically and the evolution of the adsorption intensity with electron density is studied.

cond-mat↗