-
[show abstract]
[hide abstract]
ABSTRACT: 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.
06/2011;
-
[show abstract]
[hide abstract]
ABSTRACT: 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.
03/2011;
-
[show abstract]
[hide abstract]
ABSTRACT: 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.
11/2010;
-
[show abstract]
[hide abstract]
ABSTRACT: 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 quasiparticles with multiple dark states, termed spinor slow-light polaritons. 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. Particularly, this allows the implementation of the random-mass Dirac model for which localized zero-energy (midgap) states exist with unusual long-range correlations.
Physical Review Letters 10/2010; 105(17):173603. · 7.37 Impact Factor
-
R. G. Unanyan
[show abstract]
[hide abstract]
ABSTRACT: 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 timescale τ that is inversely proportional to the boundary size of the subsystem, that is, 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 one-dimensional spin lattice system as well as a pair of coupled spin ladders obtained from numerical simulations.
Phys. Rev. A. 02/2010; 81(2).
-
[show abstract]
[hide abstract]
ABSTRACT: We describe a method to create effective gauge potentials for stationary-light polaritons. When stationary light is created in the interaction with a rotating ensemble of coherently driven double-Lambda type atoms, the equation of motion is that of a massive Schrödinger particle in a magnetic field. 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 up the possibility to study the bosonic analogue of the fractional quantum Hall effect for interacting stationary-light polaritons.
Physical Review Letters 01/2010; 104(3):033903. · 7.37 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: 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 $1 - (t/\tau)^2$, i.e. quadratically in time, with a characteristic time scale $\tau$ 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. Comment: some minor additions, 6 pages, 3 figures
10/2009;
-
[show abstract]
[hide abstract]
ABSTRACT: 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 realization of such a system is proposed.
Phys. Rev. A. 04/2009; 79(4).
-
[show abstract]
[hide abstract]
ABSTRACT: We discuss the properties of 1D stationary pulses of light in an atomic ensemble with electromagnetically induced transparency in the limit of tight spatial confinement. When the size of the wave packet becomes comparable or smaller than the absorption length of the medium, it must be described by a two-component vector which obeys the one-dimensional two-component Dirac equation with an effective mass m;{*} and effective speed of light c;{*}. Then a fundamental lower limit to the spatial width in an external potential arises from Klein tunneling and is given by the effective Compton length lambda_{C}=variant Planck's over 2pi/(m;{*}c;{*}). Since c;{*} and m;{*} can be externally controlled and can be made small, it is possible to observe effects of the relativistic dispersion for rather low energies or correspondingly on macroscopic length scales.
Physical Review Letters 03/2009; 102(6):063602. · 7.37 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: 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. Comment: 2 pages
01/2009;
-
[show abstract]
[hide abstract]
ABSTRACT: We present a general scheme to determine the loss-free adiabatic eigensolutions (dark-state polaritons) of the interaction of multiple probe laser beams with a coherently driven atomic ensemble under conditions of electromagnetically induced transparency. To this end we generalize the Morris-Shore transformation to linearized Heisenberg-Langevin equations describing the coupled light-matter system in the weak excitation limit. For the simple lambda-type coupling scheme the generalized Morris-Shore transformation reproduces the dark-state polariton solutions of slow light. Here we treat a closed-loop dual-V scheme wherein two counterpropagating control fields generate a quasistationary pattern of two counterpropagating probe fields—so-called stationary light. We show that contrary to previous predictions, there exists a single unique dark-state polariton; it obeys a simple propagation equation.
Phys. Rev. A. 06/2008; 77(6).
-
[show abstract]
[hide abstract]
ABSTRACT: We derive an integral convex combination of product states for a range of separable Werner states. Our method consists of expanding the sought-after local density operators in terms of Wigner operators. For dimension d=2, our decomposition holds for the whole separable range of Werner states, while for d>2 it is valid for a subset of separable Werner states. We illustrate the general method with the explicit examples d=2 and d=3.
04/2007;
-
[show abstract]
[hide abstract]
ABSTRACT: We describe the use of a special interaction symmetry for the robust generation of the totally symmetric superposition state or entangled state of an N-state system. The required symmetry of the Hamiltonian is that of a circulant matrix. Such a matrix has the important property that its eigenstates are independent of the matrix elements as long as the circulant symmetry is maintained. One of the eigenvectors is the target superposition. By inducing a slow evolution of the Hamiltonian into the circulant form, adiabatic following will generate the desired superposition out of a convenient initial state such as a product state. The creation process is robust: it is insensitive to details of the interaction as long as the final Hamiltonian has the required symmetry. We illustrate the procedure with a simple example: a ring of quantum wells that permit interwell tunneling, into which a single atom is placed. By carrying out adiabatic evolution the state vector approaches an equal distribution of probability amplitudes in each well.
Phys. Rev. A. 02/2007; 75(2).
-
[show abstract]
[hide abstract]
ABSTRACT: We study the ground-state entanglement of one-dimensional harmonic chains that are coupled to each other by a collective interaction as realized e.g. in an anisotropic ion crystal. Due to the collective type of coupling, where each chain interacts with every other one in the same way,the total system shows critical behavior in the direction orthogonal to the chains while the isolated harmonic chains can be gapped and non-critical. We derive lower and most importantly upper bounds for the entanglement,quantified by the von Neumann entropy, between a compact block of oscillators and its environment. For sufficiently large size of the subsystems the bounds coincide and show that the area law for entanglement is violated by a logarithmic correction.
10/2006;
-
[show abstract]
[hide abstract]
ABSTRACT: We discuss the relation between entanglement and criticality in translationally invariant harmonic lattice systems with nonrandom, finite-range interactions. We show that the criticality of the system as well as validity or breakdown of the entanglement area law are solely determined by the analytic properties of the spectral function of the oscillator system, which can easily be computed. In particular, for finite-range couplings we find a one-to-one correspondence between an area-law scaling of the bipartite entanglement and a finite correlation length. This relation is strict in the one-dimensional case and there is strong evidence for the multidimensional case. We also discuss generalizations to couplings with infinite range. Finally, to illustrate our results, a specific 1D example with nearest and next-nearest-neighbor coupling is analyzed.
Physical Review Letters 01/2006; 95(26):260604. · 7.37 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: Bipartite and global entanglement are analyzed for the ground state of a system of N spin-1∕2 particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick Hamiltonian. Under certain conditions, which include the special case of supersymmetry, the ground state can be constructed analytically. In the case of antiferromagnetic coupling and for an even number of particles, the system has a finite energy gap and the ground state undergoes a smooth transition, as a function of the continuous anisotropy parameter γ, from a separable (γ=∞) to a maximally entangled state (γ=0). From the analytic expression for the ground state, the bipartite entanglement between two subsets of spins as well as the global entanglement are calculated. Despite the absence of a quantum phase transition a discontinuous change of the scaling of the bipartite entanglement with the number of spins in the subsystem is found at the isotropy point γ=0: While at γ=0 the entanglement grows logarithmically with the system size with no upper bound, it saturates for γ≠0 at a level only depending on γ.
Phys. Rev. A. 08/2005; 72(2).
-
[show abstract]
[hide abstract]
ABSTRACT: We discuss the relation between entanglement and criticality in translationally invariant harmonic lattice systems with non-randon, finite-range interactions. We show that the criticality of the system as well as validity or break-down of the entanglement area law are solely determined by the analytic properties of the spectral function of the oscillator system, which can easily be computed. In particular for finite-range couplings we find a one-to-one correspondence between an area-law scaling of the bi-partite entanglement and a finite correlation length. This relation is strict in the one-dimensional case and there is strog evidence for the multi-dimensional case. We also discuss generalizations to couplings with infinite range. Finally, to illustrate our results, a specific 1D example with nearest and next-nearest neighbor coupling is analyzed. Comment: 4 pages, one figure, revised version
06/2005;
-
[show abstract]
[hide abstract]
ABSTRACT: Bipartite and global entanglement are analyzed for the ground state of a system of $N$ spin 1/2 particles interacting via a collective spin-spin coupling described by the Lipkin-Meshkov-Glick (LMG) Hamiltonian. Under certain conditions which includes the special case of a super-symmetry, the ground state can be constructed analytically. In the case of an anti-ferromagnetic coupling and for an even number of particles this state undergoes a smooth crossover as a function of the continuous anisotropy parameter $\gamma $ from a separable ($\gamma =\infty $) to a maximally entangled many-particle state ($\gamma =0$). From the analytic expression for the ground state, bipartite and global entanglement are calculated. In the thermodynamic limit a discontinuous change of the scaling behavior of the bipartite entanglement is found at the isotropy point $\gamma =0$. For $% \gamma =0$ the entanglement grows logarithmically with the system size with no upper bound, for $\gamma \neq 0$ it saturates at a level only depending on $\gamma $. For finite systems with total spin $J=N/2$ the scaling behavior changes at $\gamma =\gamma _{\mathrm{crit}}=1/J$.
01/2005;
-
[show abstract]
[hide abstract]
ABSTRACT: A general scheme for an adiabatic geometric phase gate is proposed which is maximally robust against parameter fluctuations. While in systems with SU(2) symmetry geometric phases are usually accompanied by dynamical phases and are thus not robust, we show that in the more general case of a SU(2) x SU(2) symmetry it is possible to obtain a non-vanishing geometric phase without dynamical contributions. The scheme is illustrated for a phase gate using two systems with dipole-dipole interactions in external laser fields which form an effective four-level system. Comment: 4 pages, 5 figures
08/2003;
-
[show abstract]
[hide abstract]
ABSTRACT: We discuss a decoherence insensitive method to create many-particle entanglement in a spin system with controllable collective interactions and propose an implementation in an ion trap. An adiabatic change of parameters allows a transfer from separable to a large variety of entangled eigenstates. We show that the Hamiltonian can have a supersymmetry permitting an explicit construction of the ground state at all times. Of particular interest is a transition in a nondegenerate ground state with a finite energy gap since here the influence of collective as well as individual decoherence mechanisms is substantially reduced. A lower bound for the energy gap is given.
Physical Review Letters 05/2003; 90(13):133601. · 7.37 Impact Factor
