33 research outputs found
Supersymmetry in quantum optics and in spin-orbit coupled systems
Light-matter interaction is naturally described by coupled bosonic and
fermionic subsystems. This suggests that a certain Bose-Fermi duality is
naturally present in the fundamental quantum mechanical description of photons
interacting with atoms. We reveal submanifolds in parameter space of a basic
light-matter interacting system where this duality is promoted to a
supersymmetry (SUSY) which remains unbroken. We show that SUSY is robust with
respect to decoherence and dissipation. In particular, a stationary density
matrix at the supersymmetric lines in the parameter space has a degenerate
subspace. A dimension of this subspace is given by the Witten index and thus
topologically protected. As a consequence of this SUSY, dissipative dynamics at
the supersymmetric lines is constrained by an additional conserved quantity
which translates some part of information about an initial state into the
stationary state subspace. We also demonstrate a robustness of this additional
conserved quantity away from the supersymmetric lines. In addition, we
demonstrate that the same SUSY structures are present in condensed matter
systems with spin-orbit couplings of Rashba and Dresselhaus types, and
therefore spin-orbit coupled systems at the SUSY lines should be robust with
respect to various types of disorder and decoherences. Our findings suggest
that optical and condensed matter systems at the SUSY points can be used for
quantum information technology and can open an avenue for quantum simulation of
the SUSY field theories.Comment: 15 pages, 3 figure
Enabling Adiabatic Passages Between Disjoint Regions in Parameter Space through Topological Transitions
We explore topological transitions in parameter space in order to enable
adiabatic passages between regions adiabatically disconnected within a given
parameter manifold. To this end, we study the Hamiltonian of two coupled qubits
interacting with external magnetic fields, and make use of the analogy between
the Berry curvature and magnetic fields in parameter space, with spectrum
degeneracies associated to magnetic charges. Symmetry-breaking terms induce
sharp topological transitions on these charge distributions, and we show how
one can exploit this effect to bypass crossing degeneracies. We also
investigate the curl of the Berry curvature, an interesting but as of yet not
fully explored object, which together with its divergence uniquely defines this
field. Finally, we suggest a simple method for measuring the Berry curvature,
thereby showing how one can experimentally verify our results.Comment: 17 pages, 11 figure
Geodesic Paths for Quantum Many-Body Systems
We propose a method to obtain optimal protocols for adiabatic ground-state
preparation near the adiabatic limit, extending earlier ideas from [D. A. Sivak
and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)] to quantum
non-dissipative systems. The space of controllable parameters of isolated
quantum many-body systems is endowed with a Riemannian quantum metric
structure, which can be exploited when such systems are driven adiabatically.
Here, we use this metric structure to construct optimal protocols in order to
accomplish the task of adiabatic ground-state preparation in a fixed amount of
time. Such optimal protocols are shown to be geodesics on the parameter
manifold, maximizing the local fidelity. Physically, such protocols minimize
the average energy fluctuations along the path. Our findings are illustrated on
the Landau-Zener model and the anisotropic XY spin chain. In both cases we show
that geodesic protocols drastically improve the final fidelity. Moreover, this
happens even if one crosses a critical point, where the adiabatic perturbation
theory fails.Comment: 5 pages, 2 figures + 4 pages supplemen
Geodesic paths for quantum many-body systems
We propose a method to obtain optimal protocols for adiabatic ground-state preparation near the adiabatic limit, extending earlier ideas from [D. A. Sivak and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)] to quantum non-dissipative systems. The space of controllable parameters of isolated quantum many-body systems is endowed with a Riemannian quantum metric structure, which can be exploited when such systems are driven adiabatically. Here, we use this metric structure to construct optimal protocols in order to accomplish the task of adiabatic ground-state preparation in a fixed amount of time. Such optimal protocols are shown to be geodesics on the parameter manifold, maximizing the local fidelity. Physically, such protocols minimize the average energy fluctuations along the path. Our findings are illustrated on the Landau-Zener model and the anisotropic XY spin chain. In both cases we show that geodesic protocols drastically improve the final fidelity. Moreover, this happens even if one crosses a critical point, where the adiabatic perturbation theory fails.http://meetings.aps.org/link/BAPS.2016.MAR.F50.9First author draf
Exceptional and regular spectra of a generalized Rabi model
We study the spectrum of the generalized Rabi model in which co- and
counter-rotating terms have different coupling strengths. It is also equivalent
to the model of a two-dimensional electron gas in a magnetic field with Rashba
and Dresselhaus spin-orbit couplings. Like in case of the Rabi model, the
spectrum of the generalized Rabi model consists of the regular and the
exceptional parts. The latter is represented by the energy levels which cross
at certain parameters' values which we determine explicitly. The wave functions
of these exceptional states are given by finite order polynomials in the
Bargmann representation. The roots of these polynomials satisfy a Bethe ansatz
equation of the Gaudin type. At the exceptional points the model is therefore
quasi-exactly solvable. An analytical approximation is derived for the regular
part of the spectrum in the weak- and strong-coupling limits. In particular, in
the strong-coupling limit the spectrum consists of two quasi-degenerate
equidistant ladders.Comment: 15 pages, 9 figure
Geometric phase contribution to quantum non-equilibrium many-body dynamics
We study the influence of geometry of quantum systems underlying space of
states on its quantum many-body dynamics. We observe an interplay between
dynamical and topological ingredients of quantum non-equilibrium dynamics
revealed by the geometrical structure of the quantum space of states. As a
primary example we use the anisotropic XY ring in a transverse magnetic field
with an additional time-dependent flux. In particular, if the flux insertion is
slow, non-adiabatic transitions in the dynamics are dominated by the dynamical
phase. In the opposite limit geometric phase strongly affects transition
probabilities. We show that this interplay can lead to a non-equilibrium phase
transition between these two regimes. We also analyze the effect of geometric
phase on defect generation during crossing a quantum critical point.Comment: 4 pages, 3 figures. Added an appendix with supplementary informatio
Epileptic monocular nystagmus and ictal diplopia as cortical and subcortical dysfunction
AbstractWe present the case of a patient with ictal monocular nystagmus and ictal diplopia who became seizure-free after resection of a right frontal focal cortical dysplasia (FCD), type 2B. Interictal neuroophthalmological examination showed several beats of a monocular nystagmus and a spasm of the contralateral eye. An exclusively ictal monocular epileptic nystagmus could be an argument for an exclusively cortical involvement in monocular eye movement control. The interictal findings in our patient, however, argue for an irregular ictal activation of both the cortical frontal eye field and the brainstem