arXiv subjects

M. Fleischhauer

Publications and source records attributed to M. Fleischhauer.

At least 19 recordsLinked to original sources

arXiv2022

Microscopic dynamics and an effective Landau-Zener transition in the quasi-adiabatic preparation of spatially ordered states of Rydberg excitations

We examine the adiabatic preparation of spatially-ordered Rydberg excitations of atoms in finite one-dimensional lattices by frequency-chirped laser pulses, as realized in a number of recent experiments simulating quantum Ising model. Our aims are to unravel the microscopic mechanism of the phase transition from the unexcited state of atoms to the antiferromagnetic-like state of Rydberg excitations by traversing an extended gapless phase, and to estimate the preparation fidelity of the target state in a moderately sized system amenable to detailed numerical analysis. We find that, in the basis of the bare atomic states, the system climbs the ladder of Rydberg excitations predominantly along the strongest-amplitude paths towards the final ordered state. We show that, despite its complexity, the interacting many-body system can be described as an effective two-level system involving a pair of lowest-energy instantaneous collective eigenstates of the time-dependent Hamiltonian. The final preparation fidelity of the target state can then be well approximated by the Landau-Zener formula, while the nonadiabatic population leakage during the passage can be estimated using a perturbative approach applied to the instantaneous collective eigenstates.

quant-ph↗

arXiv2022

Controlled Quantized Adiabatic Transport in a superlattice Wannier-Stark ladder

The Born-Fock theorem is one of the most fundamental theorems of quantum mechanics and forms the basis for reliable and efficient navigation in the Hilbert space of a quantum system with a time-dependent Hamiltonian by adiabatic evolution. In the absence of level crossings, i.e. without degeneracies, and under adiabatic time evolution all eigenstates of the Hamiltonian keep their energetic order, labelled by a conserved integer quantum number. Thus controlling the eigenstates of the Hamiltonian and their energetic order in asymptotic limits allows to engineer a perfect adiabatic transfer between a large number of initial and target states. The fidelity of the state transfer is only limited by adiabaticity and the selection of target states is controlled by the integer invariant labelling the order of eigenstates. We here show for the example of a finite superlattice Wannier-Stark ladder, i.e. a one-dimensional lattice with alternating hopping amplitudes and constant potential gradient, that such an adiabatic control of eigenstates can be used to induce perfectly quantized single-particle transport across a pre-determined number of lattice sites. We dedicate this paper to the memory of our late friend and colleague Bruce Shore, who was an expert in adiabatic processes and taught us much about this field.

quant-ph↗

arXiv2020

Unlimited growth of particle fluctuations in many-body localized phases

We study quench dynamics in a t-V chain of spinless fermions (equivalent to the spin-1/2 Heisenberg chain) with strong potential disorder. For this prototypical model of many-body localization we have recently argued that -- contrary to the established picture -- particles do not become fully localized. Here we summarize and expand on our previous results for various entanglement measures such as the number and the Hartley number entropy. We investigate, in particular, possible alternative interpretations of our numerical data. We find that none of these alternative interpretations appears to hold and, in the process, discover further strong evidence for the absence of localization. Furthermore, we obtain more insights into the entanglement dynamics and the particle fluctuations by comparing with non-interacting systems where we derive several strict bounds. We find that renormalized versions of these bounds also hold in the interacting case where they provide support for numerically discovered scaling relations between number and entanglement entropies.

cond-mat.dis-nn↗

arXiv2019

Absence of topology in Gaussian mixed states of bosons

In a recent paper [Bardyn et al. Phys. Rev. X 8, 011035 (2018)], it was shown that the generalization of the many-body polarization to mixed states can be used to construct a topological invariant which is also applicable to finite-temperature and non-equilibrium Gaussian states of lattice fermions. The many-body polarization defines an ensemble geometric phase (EGP) which is identical to the Zak phase of a fictitious Hamiltonian, whose symmetries determine the topological classification. Here we show that in the case of Gaussian states of bosons the corresponding topological invariant is always trivial. This also applies to finite-temperature states of bosons in lattices with a topologically non-trivial band-structure. As a consequence there is no quantized topological charge pumping for translational invariant bulk states of non-interacting bosons.

quant-ph↗

arXiv2018

The fate of dynamical phase transitions at finite temperatures and in open systems

When a quantum system is quenched from its ground state, the time evolution can lead to non-analytic behavior in the return rate at critical times $t_c$. Such dynamical phase transitions (DPT's) can occur, in particular, for quenches between phases with different topological properties in Gaussian models. In this paper we discuss Loschmidt echos generalized to density matrices and obtain results for quenches in closed Gaussian models at finite temperatures as well as for open system dynamics described by a Lindblad master equation. While cusps in the return rate are always smoothed out by finite temperatures we show that dissipative dynamics can be fine-tuned such that DPT's persist.

cond-mat.stat-mech↗

arXiv2016

Mesoscopic Rydberg-blockaded ensembles in the superatom regime and beyond

Controlling strongly interacting many-body systems enables the creation of tailored quantum matter, with properties transcending those based solely on single particle physics. Atomic ensembles which are optically driven to a Rydberg state provide many examples of this, such as atom-atom entanglement, many-body Rabi oscillations, strong photon-photon interaction and spatial pair correlations. In its most basic form, Rydberg quantum matter consists of an isolated ensemble of strongly interacting atoms spatially confined to the blockade volume - a so-called superatom. Here we demonstrate the controlled creation and characterization of an isolated mesoscopic superatom by means of accurate density engineering and excitation to Rydberg $p$-states. Its variable size allows to investigate the transition from effective two-level physics for strong confinement to many-body phenomena in extended systems. By monitoring continuous laser-induced ionization we observe a strongly anti-bunched ion emission under blockade conditions and extremely bunched ion emission under off-resonant excitation. Our experimental setup enables in vivo measurements of the superatom, yielding insight into both excitation statistics and dynamics. We anticipate straightforward applications in quantum optics and quantum information as well as future experiments on many-body physics.

physics.atom-ph↗

arXiv2012

Spatio-temporal Fermionization of Strongly Interacting 1D Bosons

Building on the recent experimental achievements obtained with scanning electron microscopy on ultracold atoms, we study one-dimensional Bose gases in the crossover between the weakly (quasi-condensate) and the strongly interacting (Tonks-Girardeau) regime. We measure the temporal two-particle correlation function and compare it with calculations performed using the Time Evolving Block Decimation algorithm. More pronounced antibunching is observed when entering the more strongly interacting regime. Even though this mimics the onset of a fermionic behavior, we highlight that the exact and simple duality between 1D bosons and fermions does not hold when such dynamical response is probed. The onset of fermionization is also reflected in the density distribution, which we measure \emph{in situ} to extract the relevant parameters and to identify the different regimes. Our results show agreement between experiment and theory and give new insight into the dynamics of strongly correlated many-body systems.

cond-mat.quant-gas↗

arXiv2012

From Anderson to anomalous localization in cold atomic gases with effective spin-orbit coupling

We study the dynamics of a one-dimensional spin-orbit coupled Schrodinger particle with two internal components moving in a random potential. We show that this model can be implemented by the interaction of cold atoms with external lasers and additional Zeeman and Stark shifts. By direct numerical simulations a crossover from an exponential Anderson-type localization to an anomalous power-law behavior of the intensity correlation is found when the spin-orbit coupling becomes large. The power-law behavior is connected to a Dyson singularity in the density of states emerging at zero energy when the system approaches the quasi-relativistic limit of the random mass Dirac model. We discuss conditions under which the crossover is observable in an experiment with ultracold atoms and construct explicitly the zero-energy state, thus proving its existence under proper conditions.

cond-mat.quant-gas↗

arXiv2011

Entanglement Dynamics in Harmonic Oscillator Chains

We study the long-time evolution of the bipartite entanglement in translationally invariant gapped harmonic lattice systems with finite-range interactions. A lower bound for the von Neumann entropy is derived in terms of the purity of the reduced density matrix. It is shown that starting from an initially Gaussian state the entanglement entropy increases at least linearly in time. This implies that the dynamics of gapped (non-critical) harmonic lattice systems cannot be efficiently simulated by algorithms based on matrix-product decompositions of the quantum state.

quant-ph↗

arXiv2011

Photonic band-gap properties for two-component slow light

We consider two-component "spinor" slow light in an ensemble of atoms coherently driven by two pairs of counterpropagating control laser fields in a double tripod-type linkage scheme. We derive an equation of motion for the spinor slow light (SSL) representing an effective Dirac equation for a massive particle with the mass determined by the two-photon detuning. By changing the detuning the atomic medium acts as a photonic crystal with a controllable band gap. If the frequency of the incident probe light lies within the band gap, the light tunnels through the sample. For frequencies outside the band gap, the transmission probability oscillates with increasing length of the sample. In both cases the reflection takes place into the complementary mode of the probe field. We investigate the influence of the finite excited state lifetime on the transmission and reflection coefficients of the probe light. We discuss possible experimental implementations of the SSL using alkali atoms such as Rubidium or Sodium.

quant-ph↗

arXiv2010

Spinor Slow-Light and Dirac particles with variable mass

We consider the interaction of two weak probe fields of light with an atomic ensemble coherently driven by two pairs of standing wave laser fields in a tripod-type linkage scheme. The system is shown to exhibit a Dirac-like spectrum for light-matter quasi-particles with multiple dark-states, termed spinor slow-light polaritons (SSP). They posses an "effective speed of light" given by the group-velocity of slow-light, and can be made massive by inducing a small two-photon detuning. Control of the two-photon detuning can be used to locally vary the mass including a sign flip. This allows e.g. the implementation of the random-mass Dirac model for which localized zero-energy (mid-gap) states exist with unsual long-range correlations.

quant-ph↗

arXiv2010

Quantum emitters coupled to surface plasmons of a nano-wire: A Green function approach

We investigate a system consisting of a single, as well as two emitters strongly coupled to surface plasmon modes of a nano-wire using a Green function approach. Explicit expressions are derived for the spontaneous decay rate into the plasmon modes and for the atom-plasmon coupling as well as a plasmon-mediated atom-atom coupling. Phenomena due to the presence of losses in the metal are discussed. In case of two atoms, we observe Dicke sub- and superradiance resulting from their plasmon-mediated interaction. Based on this phenomenon, we propose a scheme for a deterministic two-qubit quantum gate. We also discuss a possible realization of interesting many-body Hamiltonians, such as the spin-boson model, using strong emitter-plasmon coupling.

quant-ph↗

arXiv2010

Short-time vs. long-time dynamics of entanglement in quantum lattice models

We study the short-time evolution of the bipartite entanglement in quantum lattice systems with local interactions in terms of the purity of the reduced density matrix. A lower bound for the purity is derived in terms of the eigenvalue spread of the interaction Hamiltonian between the partitions. Starting from an initially separable state the purity decreases as $1 - (t/τ)^2$, i.e. quadratically in time, with a characteristic time scale $τ$ that is inversly proportional to the boundary size of the subsystem, i.e., as an area-law. For larger times an exponential lower bound is derived corresponding to the well-known linear-in-time bound of the entanglement entropy. The validity of the derived lower bound is illustrated by comparison to the exact dynamics of a 1D spin lattice system as well as a pair of coupled spin ladders obtained from numerical simulations.

quant-ph↗

arXiv2009

Effective magnetic fields for stationary light

We describe a method to create effective gauge potentials for stationary-light polaritons in two or three spatial dimensions. When stationary light is created in the interaction with a uniformly rotating ensemble of coherently driven double $Λ$ atoms, the equation of motion is that of a massive Schrödinger particle in an effective magnetic field. In addition a repulsive scalar potential emerges which can however be compensated by a space-dependent detuning. Since the effective interaction area for the polaritons can be made large, degenerate Landau levels can be created with degeneracy well above 100. This opens the possibility to study the bosonic analogue of the fractional quantum Hall effect for interacting stationary-light polaritons.

quant-ph↗

arXiv2009

Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation

The applicability of the so-called truncated Wigner approximation (-W) is extended to multitime averages of Heisenberg field operators. This task splits naturally in two. Firstly, what class of multitime averages the -W approximates, and, secondly, how to proceed if the average in question does not belong to this class. To answer the first question we develop an (in principle, exact) path-integral approach in phase-space based on the symmetric (Weyl) ordering of creation and annihilation operators. These techniques calculate a new class of averages which we call time-symmetric. The -W equations emerge as an approximation within this path-integral techniques. We then show that the answer to the second question is associated with response properties of the system. In fact, for two-time averages Kubo's renowned formula relating the linear response function to two-time commutators suffices. The -W is trivially generalised to the response properties of the system allowing one to calculate approximate time-normally ordered two-time correlation functions with surprising ease. The techniques we develop are demonstrated for the Bose-Hubbard model.

cond-mat.stat-mech↗

arXiv2009

Simulation of a quantum phase transition of polaritons with trapped ions

We present a novel system for the simulation of quantum phase transitions of collective internal qubit and phononic states with a linear crystal of trapped ions. The laser-ion interaction creates an energy gap in the excitation spectrum, which induces an effective phonon-phonon repulsion and a Jaynes-Cummings-Hubbard interaction. This system shows features equivalent to phase transitions of polaritons in coupled cavity arrays. Trapped ions allow for easy tunabilty of the hopping frequency by adjusting the axial trapping frequency, and the phonon-phonon repulsion via the laser detuning and intensity. We propose an experimental protocol to access all observables of the system, which allows one to obtain signatures of the quantum phase transitions even with a small number of ions.

quant-ph↗

arXiv2009

Qubit protection in nuclear-spin quantum dot memories

We present a mechanism to protect quantum information stored in an ensemble of nuclear spins in a semiconductor quantum dot. When the dot is charged the nuclei interact with the spin of the excess electron through the hyperfine coupling. If this coupling is made off-resonant it leads to an energy gap between the collective storage states and all other states. We show that the energy gap protects the quantum memory from local spin-flip and spin-dephasing noise. Effects of non-perfect initial spin polarization and inhomogeneous hyperfine coupling are discussed.

cond-mat.mes-hall↗

arXiv2009

Confinement limit of Dirac particles in scalar 1D potentials

We present a general proof that Dirac particles cannot be localized below their Compton length by symmetric but otherwise arbitrary scalar potentials. This proof does not invoke the Heisenberg uncertainty relation and thus does not rely on the nonrelativistic linear momentum relation. Further it is argued that the result is also applicable for more general potentials, as e.g. generated by nonlinear interactions. Finally a possible realisation of such a system is proposed.

quant-ph↗