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Shimon Levit

Publications and source records attributed to Shimon Levit.

17 recordsLinked to original sources
arXiv2023

Quantum Mechanics Lecture Notes. Selected Chapters

These are extended lecture notes of the quantum mechanics course which I am teaching in the Weizmann Institute of Science graduate physics program. They cover the topics listed below. The first four chapter are posted here. Their content is detailed on the next page. The other chapters are planned to be added in the coming months. 1. Motion in External Electromagnetic Field. Gauge Fields in Quantum Mechanics. 2. Quantum Mechanics of Electromagnetic Field 3. Photon-Matter Interactions 4. Quantization of the Schr\"odinger Field (The Second Quantization) 5. Open Systems. Density Matrix 6. Adiabatic Theory. The Berry Phase. The Born-Oppenheimer Approximation 7. Mean Field Approaches for Many Body Systems -- Fermions and Bosons

quant-ph↗
arXiv2020

Variational Approach to Tunneling Dynamics. Application to Hot Superfluid Fermi Systems. Spontaneous and Induced Fission

We introduce a general variational framework to address the tunneling of hot Fermi systems. We use the representation of the trace of the imaginary time $\tau=it$ propagator as a functional integral type of a sum over complete sets of states at intermediate propagation slices. We assume that these states are $\tau$-dependent and generated by an arbitrary trial Hamiltonian $H_0(\tau)$. We then use the convexity inequality to derive $H_0(\tau)$ controlled variational bound for a trial action functional. This functional has a general structure consisting of two parts - statistically weighted quantum penetrability and dynamical tunneling entropy. We examine how this structure incorporates the basic physics of tunneling of hot Fermi systems. Using the variational inequality one can optimise the dynamical parameters controlling the action functional for any choice of the trial problem. As an application we take $H_0(\tau)$ to describe imaginary time dynamics of non interacting Bogoliubov-de Gennes (BdG) quasiparticles. Optimising its dynamical parameters we extend the tunneling theory of hot Fermi systems to the Hartree-Fock-Bogoliubov(HFB) frame and derive the corresponding generalisation of imaginary time temperature dependent BdG mean field equations. As in the trial action the prominent feature of these equations is an inseparable interplay between quantum dynamical and entropic statistical effects. In the zero temperature limit these equations describe the "false ground state" tunneling decay of superfluid Fermi systems (spontaneous fission in nuclear physics). With increasing excitation energy (effective temperature) the decay process is gradually evolving from pure quantum tunneling to statistical "bottle neck" escape mechanism.

nucl-th↗
arXiv2011

Feshbach resonances and their interaction in light scattering off photonic crystal slabs

The concept of Feshbach resonances developed for quantum mechanical scattering is applied in the analysis of classical light scattering off photonic crystal slabs. It is shown that this concept can be realized almost perfectly in these systems. As an application guided-mode resonances in the grating waveguide structure (GWS) are studied in detail. Using simple resonance dominance approximation the characteristic properties of isolated Feshbach resonances in light scattering are exhibited. Formation and interaction of overlapping resonances are investigated. The relevant parameters of the GWS are identified which control the shape of the reflectivity of interacting resonances as well as the enhancement of the electromagnetic field. The differences in the properties of TE and TM resonances is emphasized for both isolated and interacting resonances.

physics.optics↗
arXiv2009

Path Integrals for Photonic Crystals

We develop a path integrals approach for analyzing stationary light propagation appropriate for photonic crystals. The hermitian form of the stationary Maxwell equations is transformed into a quantum mechanical problem of a spin 1 particle with spin-orbit coupling and position dependent mass. After appropriate ordering several path integral representations of a solution are constructed. One leaves the propagation of polarization degrees of freedom in an operator form integrated over paths in coordinate space. The use of spin 1 coherent states allows to represent this part as a path integral over such states. Finally a path integral in transversal momentum space with explicit transversality enforced at every time slice is also given. As an example the geometrical optics limit is discussed and the ray equation is recovered together with the Rytov rotation of the polarization vector.

physics.optics↗
arXiv2009

Qubit Coherent Control with Squeezed Light Fields

We study the use of squeezed light for qubit coherent control and compare it with the coherent state control field case. We calculate the entanglement between a short pulse of resonant squeezed light and a two-level atom in free space and the resulting operation error. We find that the squeezing phase, the phase of the light field and the atomic superposition phase, all determine whether atom-pulse mode entanglement and the gate error are enhanced or suppressed. However, when averaged over all possible qubit initial states, the gate error would not decrease by a practicably useful amount and would in fact increase in most cases. We discuss the possibility of measuring the increased gate error as a signature of the enhancement of entanglement by squeezing.

quant-ph↗
arXiv2008

Coherent optical control of correlation waves of spins in semiconductors

We calculate the dynamical fluctuation spectrum of electronic spins in a semiconductor under a steady-state illumination by light containing polarization squeezing correlations. Taking into account quasi-particle lifetime and spin relaxation for this non-equilibrium situation we consider up to fourth order optical effects which are sensitive to the squeezing phases. We demonstrate the possibility to control the spin fluctuations by optically modulating these phases as a function of frequency, leading to a non-Lorentzian spectrum which is very different from the thermal equilibrium fluctuations in n-doped semiconductors. Specifically, in the time-domain spin-spin correlation can exhibit time delays and sign flips originating from the phase modulations and correlations of polarizations, respectively. For higher light intensity we expect a regime where the squeezing correlations will dominate the spectrum.

cond-mat.other↗
arXiv2006

Atom in a coherently controlled squeezed vacuum

A broadband squeezed vacuum photon field is characterized by a complex squeezing function. We show that by controlling the wavelength dependence of its phase it is possible to change the dynamics of the atomic polarization interacting with the squeezed vacuum. Such a phase modulation effectively produces a finite range temporal interaction kernel between the two quadratures of the atomic polarization yielding the change in the decay rates as well as the appearance of additional oscillation frequencies. We show that decay rates slower than the spontaneous decay rate can be achieved even for a squeezed bath in the classic regime. For linear and quadratic phase modulations the power spectrum of the scattered light exhibits narrowing of the central peak due to the modified decay rates. For strong phase modulations side lobes appear symmetrically around the central peak reflecting additional oscillation frequencies.

quant-ph↗
arXiv2005

Semiconductor Microstructure in a Squeezed Vacuum: Electron-Hole Plasma Luminescence

We consider a semiconductor quantum-well placed in a wave guide microcavity and interacting with the broadband squeezed vacuum radiation, which fills one mode of the wave guide with a large average occupation. The wave guide modifies the optical density of states so that the quantum well interacts mostly with the squeezed vacuum. The vacuum is squeezed around the externally controlled central frequency $\om_0$, which is tuned above the electron-hole gap $E_g$, and induces fluctuations in the interband polarization of the quantum-well. The power spectrum of scattered light exhibits a peak around $\om_0$, which is moreover non-Lorentzian and is a result of both the squeezing and the particle-hole continuum. The squeezing spectrum is qualitatively different from the atomic case. We discuss the possibility to observe the above phenomena in the presence of additional non-radiative (e-e, phonon) dephasing.

cond-mat.mes-hall↗
arXiv2002

Controlled Dephasing of a Quantum Dot in the Kondo Regime

In this work we analyze how coherent transport through a Quantum Dot (QD) in the Kondo regime is affected by the weak capacitive interaction with a nearby biased Quantum Point Contact (QPC). We find that when the QD-QPC interaction is weak the width of the Kondo resonance is hardly affected by it. However, the spectral weight of the Kondo peak is reduced leading to an observable suppression of the conductance and the elastic transmission probability through the QD.

cond-mat.mes-hall↗
arXiv2001

Universal Features of Interacting Chaotic Quantum Dots. Application to Statistics of Coulomb Blockade Peak Spacings

We present a complete classification of the electron-electron interaction in chaotic quantum dots based on expansion in inverse powers of $1/M$, the number of the electron states in the Thouless window, $M \simeq k_F R$. This classification is quite universal and extends and enlarges the universal non interacting RMT statistical ensembles. We show that existing Coulomb blockade peak spacing data for $B=0$ and $B\ne 0$ is described quite accurately by the interacting GSE and by its extension to $B\ne 0$. The bimodal structure existing in the interacting GUE case is completely washed out by the combined effect of the spin orbit, pairing and higher order residual interactions.

cond-mat.mes-hall↗
arXiv2001

Effects of Entanglement in Controlled Dephasing

In controlled dephasing as a result of the interaction of a controlled environment (dephasor) and the system under observation (dephasee) the states of the two subsystems are entangled. Using as an example the ``Which Path Detector'', we discuss how the entanglement influences the controlled dephasing. In particular, we calculate the suppression $ν$ of A-B oscillations as a function of the bias $eV$ applied to the QPC and the coupling $Γ$ of the QD to the leads. At low temperatures the entanglement produces a smooth crossover from $ν\propto (eV/Γ)^2$, when $eV \ll Γ$ to $ν\propto eV/Γ$, for $eV \gg Γ$.

cond-mat.mes-hall↗
arXiv1999

Statistics of Hartree-Fock Levels in Small Disordered Systems

We study the statistics of quasiparticle and quasihole levels in small interacting disordered systems within the Hartree-Fock approximation. The distribution of the inverse compressibility, given according to Koopmans' theorem by the distance between the two levels across the Fermi energy, evolves from a Wigner distribution in the non-interacting limit to a shifted Gaussian for strong interactions. On the other hand the nature of the distribution of spacings between neighboring levels on the same side of the Fermi energy (corresponding to energy differences between excited states of the system with one missing or one extra electron) is not affected by the interaction and follows Wigner-Dyson statistics. These results are derived analytically by isolating and solving the appropriate Hartree-Fock equations for the two levels. They are substantiated by numerical simulations of the full set of Hartree-Fock equations for a disordered quantum dot with Coulomb interactions. We find enhanced fluctuations of the inverse compressibility compared to the prediction of Random Matrix Theory, possibly due to localization of the wavefunctions around the edge of the dot. The distribution of the inverse compressibility calculated from the discrete second derivative with respect to the number of particles of the Hartree-Fock ground state energy deviates from the distribution of the level spacing across the Fermi energy. The two distributions have similar shapes but are shifted with respect to each other. The deviation increases with the strength of the interaction thus indicating the breakdown of Koopmans' theorem in the strongly interacting limit.

cond-mat.mes-hall↗
arXiv1996

Variational Master Field for Large-N Interacting Matrix Models - Free Random Variables on Trial

Matrices are said to behave as free non-commuting random variables if the action which governs their dynamics constrains only their eigenvalues, i.e. depends on traces of powers of individual matrices. The authors use recently developed mathematical techniques in combination with a standard variational principle to formulate a new variational approach for matrix models. Approximate variational solutions of interacting large-N matrix models are found using the free random matrices as the variational space. Several classes of classical and quantum mechanical matrix models with different types of interactions are considered and the variational solutions compared with exact Monte Carlo and analytical results. Impressive agreement is found in a majority of cases.

hep-th↗
arXiv1996

Parametric Excitation of Edge Waves in the Quantum Hall Effect

We consider the process of parametric excitation of gapless edge modes in a Hall bar by an alternating current. We find that such a process can be realized provided both an inter-edge interaction and a constant current are present in the bar. The expected experimental signatures of this phenomenon are discussed.

cond-mat↗
arXiv1995

Coulomb Drag of Edge Excitations in the Chern-Simons Theory of the Fractional Quantum Hall Effect

Long range Coulomb interaction between the edges of a Hall bar changes the nature of the gapless edge excitations. Instead of independent modes propagating in opposite directions on each edge as expected for a short range interaction one finds elementary excitations living simultaneously on both edges, i.e. composed of correlated density waves propagating in the same direction on opposite edges. We discuss the microscopic features of this Coulomb drag of excitations in the fractional quantum Hall regime within the framework of the bosonic Chern-Simons Landau-Ginzburg theory. The dispersion law of these novel excitations is non linear and depends on the distance between the edges as well as on the current that flows through the sample. The latter dependence indicates a possibility of parametric excitation of these modes. The bulk distributions of the density and currents of the edge excitations differ significantly for short and long range interactions.

cond-mat↗
arXiv1993

Body Fixed Frame, Rigid Gauge Rotations and Large N Random Fields in QCD

The "body fixed frame" with respect to local gauge transformations is introduced. Rigid gauge "rotations" in QCD and their \Sch equation are studied for static and dynamic quarks. Possible choices of the rigid gauge field configuration corresponding to a nonvanishing static colormagnetic field in the "body fixed" frame are discussed. A gauge invariant variational equation is derived in this frame. For large number N of colors the rigid gauge field configuration is regarded as random with maximally random probability distribution under constraints on macroscopic--like quantities. For the uniform magnetic field the joint probability distribution of the field components is determined by maximizing the appropriate entropy under the area law constraint for the Wilson loop. In the quark sector the gauge invariance requires the rigid gauge field configuration to appear not only as a background but also as inducing an instantaneous quark-quark interaction. Both are random in the large N limit.

hep-th↗