arXiv subjects

T. Gasenzer

Publications and source records attributed to T. Gasenzer.

At least 19 recordsLinked to original sources

arXiv2019

Stability analysis of ground states in a one-dimensional trapped spin-1 Bose gas

In this work we study the stability properties of the ground states of a spin-1 Bose gas in presence of a trapping potential in one spatial dimension. To set the stage we first map out the phase diagram for the trapped system by making use of a, so-called, continuous-time Nesterov method. We present an extension of the method, which has been previously applied to one-component systems, to our multi-component system. We show that it is a powerful and robust tool for finding the ground states of a physical system without the need of an accurate initial guess. We subsequently solve numerically the Bogoliubov de-Gennes equations in order to analyze the stability of the ground states of the trapped spin-1 system. We find that the trapping potential retains the overall structure of the stability diagram, while affecting the spectral details of each of the possible ground state waveforms. It is also found that the peak density of the trapped system is the characteristic quantity describing dynamical instabilities in the system. Therefore replacing the homogeneous density with the peak density of the trapped system leads to good agreement of the homogeneous Bogoliubov predictions with the numerically observed maximal growth rates of dynamically unstable modes. The stability conclusions in the one-dimensional trapped system are independent of the spin coupling strength and the normalized trap strength over several orders of magnitude of their variation.

cond-mat.quant-gas↗

arXiv2019

Violation of single-length scaling dynamics via spin vortices in an isolated spin-1 Bose gas

We consider the phase ordering dynamics of an isolated quasi-two-dimensional spin-1 Bose gas quenched into an easy-plane ferromagnetic phase. Preparing the initial system in an unmagnetized anti-ferromagnetic state the subsequent ordering involves both polar core and Mermin-Ho spin vortices, with the ratio between the different vortices controllable by the quench parameter. Ferromagnetic domain growth occurs as these vortices annihilate. The distinct dynamics of the two types of vortices means that the domain growth law is determined by two macroscopic length scales, violating the standard dynamic scaling hypothesis. Nevertheless we find that universality of the ordering process manifests in the decay laws for the spin vortices.

cond-mat.quant-gas↗

arXiv2018

Observation of universal dynamics in an isolated one-dimensional Bose gas far from equilibrium

We provide experimental evidence of universal dynamics far from equilibrium during the relaxation of an isolated one-dimensional Bose gas. Following a rapid cooling quench, the system exhibits universal scaling in time and space, associated with the approach of a non-thermal fixed point. The time evolution within the scaling period is described by a single universal function and scaling exponent, independent of the specifics of the initial state. Our results provide a quantum simulation in a regime, where to date no theoretical predictions are available. This constitutes a crucial step in the verification of universality far from equilibrium. If successful, this may lead to a comprehensive classification of systems based on their universal properties far from equilibrium, relevant for a large variety of systems at different scales.

cond-mat.quant-gas↗

arXiv2016

A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas

We use the coordinate Bethe ansatz to exactly calculate matrix elements between eigenstates of the Lieb-Liniger model of one-dimensional bosons interacting via a two-body delta-potential. We investigate the static correlation functions of the zero-temperature ground state and their dependence on interaction strength, and analyze the effects of system size in the crossover from few-body to mesoscopic regimes for up to seven particles. We also obtain time-dependent nonequilibrium correlation functions for five particles following quenches of the interaction strength from two distinct initial states. One quench is from the non-interacting ground state and the other from a correlated ground state near the strongly interacting Tonks-Girardeau regime. The final interaction strength and conserved energy are chosen to be the same for both quenches. The integrability of the model highly constrains its dynamics, and we demonstrate that the time-averaged correlation functions following quenches from these two distinct initial conditions are both nonthermal and moreover distinct from one another.

cond-mat.quant-gas↗

arXiv2013

Dynamic formation of Rydberg aggregates at off-resonant excitation

The dynamics of a cloud of ultra-cold two-level atoms is studied at off-resonant laser driving to a Rydberg state. We find that resonant excitation channels lead to strongly peaked spatial correlations associated with the buildup of asymmetric excitation structures. These aggregates can extend over the entire ensemble volume, but are in general not localized relative to the system boundaries. The characteristic distances between neighboring excitations depend on the laser detuning and on the interaction potential. These properties lead to characteristic features in the spatial excitation density, the Mandel $Q$ parameter, and the total number of excitations. As an application an implementation of the three-atom CSWAP or Fredkin gate with Rydberg atoms is discussed. The gate not only exploits the Rydberg blockade, but also utilizes the special features of an asymmetric geometric arrangement of the three atoms. We show that continuous-wave off-resonant laser driving is sufficient to create the required spatial arrangement of atoms out of a homogeneous cloud.

physics.atom-ph↗

arXiv2012

Finite-size effects in strongly interacting Rydberg gases

The scaling of the number of Rydberg excitations in a laser-driven cloud of atoms with the interaction strength is found to be affected by the finite size of the system. The scaling predicted by a theoretical model is compared with results extracted from a numerical many-body simulation. We find that the numerically obtained scaling exponent in general does not agree with the analytical prediction. By individually testing the assumptions leading to the theoretical prediction using the results from the numerical analysis, we identify the origin of the deviations, and explain it as arising from the finite size of the system. Furthermore, finite-size effects in the pair correlation function $g^{(2)}$ are predicted. Finally, in larger ensembles, we find that the theoretical predictions and the numerical results agree, provided that the system is sufficiently homogeneous.

physics.atom-ph↗

arXiv2012

Metastable states of hydrogen: their geometric phases and flux densities

We discuss the geometric phases and flux densities for the metastable states of hydrogen with principal quantum number n=2 being subjected to adiabatically varying external electric and magnetic fields. Convenient representations of the flux densities as complex integrals are derived. Both, parity conserving (PC) and parity violating (PV) flux densities and phases are identified. General expressions for the flux densities following from rotational invariance are derived. Specific cases of external fields are discussed. In a pure magnetic field the phases are given by the geometry of the path in magnetic field space. But for electric fields in presence of a constant magnetic field and for electric plus magnetic fields the geometric phases carry information on the atomic parameters, in particular, on the PV atomic interaction. We show that for our metastable states also the decay rates can be influenced by the geometric phases and we give a concrete example for this effect. Finally we emphasise that the general relations derived here for geometric phases and flux densities are also valid for other atomic systems having stable or metastable states, for instance, for He with n=2. Thus, a measurement of geometric phases may give important experimental information on the mass matrix and the electric and magnetic dipole matrices for such systems. This could be used as a check of corresponding theoretical calculations of wave functions and matrix elements.

physics.atom-ph↗

arXiv2010

Longitudinal Atomic Beam Spin Echo Experiments: A possible way to study Parity Violation in Hydrogen

We discuss the propagation of hydrogen atoms in static electric and magnetic fields in a longitudinal atomic beam spin echo (lABSE) apparatus. Depending on the choice of the external fields the atoms may acquire both dynamical and geometrical quantum mechanical phases. As an example of the former, we show first in-beam spin rotation measurements on atomic hydrogen, which are in excellent agreement with theory. Additional calculations of the behaviour of the metastable 2S states of hydrogen reveal that the geometrical phases may exhibit the signature of parity-(P-)violation. This invites for possible future lABSE experiments, focusing on P-violating geometrical phases in the lightest of all atoms.

physics.atom-ph↗

arXiv2010

Two-mode Bose gas: Beyond classical squeezing

The dynamical evolution of squeezing correlations in an ultracold Bose-Einstein distributed across two modes is investigated theoretically in the framework of the Bose-Hubbard model. It is shown that the eigenstates of the Hamiltonian do not exploit the full region allowed by Heisenberg's uncertainty relation for number and phase fluctuations. The development of non-classical correlations and relative number squeezing is studied in the transition from the Josephson to the Fock regime. Comparing the full quantum evolution with classical statistical simulations allows to identify quantum aspects of the squeezing formation. In the quantum regime, the measurement of squeezing allows to distinguish even and odd total particle numbers.

cond-mat.quant-gas↗

arXiv2009

Single-particle density matrix for a time-dependent strongly interacting one-dimensional Bose gas

We derive a $1/c$-expansion for the single-particle density matrix of a strongly interacting time-dependent one-dimensional Bose gas, described by the Lieb-Liniger model ($c$ denotes the strength of the interaction). The formalism is derived by expanding Gaudin's Fermi-Bose mapping operator up to $1/c$-terms. We derive an efficient numerical algorithm for calculating the density matrix for time-dependent states in the strong coupling limit, which evolve from a family of initial conditions in the absence of an external potential. We have applied the formalism to study contraction dynamics of a localized wave packet upon which a parabolic phase is imprinted initially.

cond-mat.quant-gas↗

arXiv2009

A computer controlled pendulum with position readout

We have designed, built and operated a physical pendulum which allows one to demonstrate experimentally the behaviour of the pendulum under any equation of motion for such a device for any initial conditions. All parameters in the equation of motion can be defined by the user. The potential of the apparatus reaches from demonstrating simple undamped harmonic oscillations to complex chaotic behaviour of the pendulum. The position data of the pendulum as well as derived kinematical quantities like velocity and acceleration can be stored for later offline analysis.

physics.pop-ph↗

arXiv2009

Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions

The asymptotic form of the wave functions describing a freely expanding Lieb-Liniger gas is derived by using a Fermi-Bose transformation for time-dependent states, and the stationary phase approximation. We find that asymptotically the wave functions approach the Tonks-Girardeau (TG) structure as they vanish when any two of the particle coordinates coincide. We point out that the properties of these asymptotic states can significantly differ from the properties of a TG gas in a ground state of an external potential. The dependence of the asymptotic wave function on the initial state is discussed. The analysis encompasses a large class of initial conditions, including the ground states of a Lieb-Liniger gas in physically realistic external potentials. It is also demonstrated that the interaction energy asymptotically decays as a universal power law with time, $E_\mathrm{int}\propto t^{-3}$.

cond-mat.other↗

arXiv2008

Parity Violation in Hydrogen and Longitudinal Atomic Beam Spin Echo I

We discuss the propagation of hydrogen atoms in static electric and magnetic fields in a longitudinal atomic beam spin echo (lABSE) apparatus. There the atoms acquire geometric (Berry) phases that exhibit a new manifestation of parity-(P-)violation in atomic physics. We provide analytical as well as numerical calculations of the behaviour of the metastable 2S states of hydrogen. The conditions for electromagnetic field configurations that allow for adiabatic evolution of the relevant atomic states are investigated. Our results provide the theoretical basis for the discussion of possible measurements of P-violating geometric phases in lABSE experiments.

physics.atom-ph↗

arXiv2007

Fermi-Bose transformation for the time-dependent Lieb-Liniger gas

Exact solutions of the Schrodinger equation describing a freely expanding Lieb-Liniger (LL) gas of delta-interacting bosons in one spatial dimension are constructed. The many-body wave function is obtained by transforming a fully antisymmetric (fermionic) time-dependent wave function which obeys the Schrodinger equation for a free gas. This transformation employs a differential Fermi-Bose mapping operator which depends on the strength of the interaction and the number of particles.

cond-mat.other↗

arXiv2007

Quantum versus classical statistical dynamics of an ultracold Bose gas

We investigate the conditions under which quantum fluctuations are relevant for the quantitative interpretation of experiments with ultracold Bose gases. This requires to go beyond the description in terms of the Gross-Pitaevskii and Hartree-Fock-Bogoliubov mean-field theories, which can be obtained as classical (statistical) field-theory approximations of the quantum many-body problem. We employ functional-integral techniques based on the two-particle irreducible (2PI) effective action. The role of quantum fluctuations is studied within the nonperturbative 2PI 1/N expansion to next-to-leading order. At this accuracy level memory-integrals enter the dynamic equations, which differ for quantum and classical statistical descriptions. This can be used to obtain a 'classicality' condition for the many-body dynamics. We exemplify this condition by studying the nonequilibrium evolution of a 1D Bose gas of sodium atoms, and discuss some distinctive properties of quantum versus classical statistical dynamics.

cond-mat.other↗

arXiv2006

Ultracold atomic quantum gases far from equilibrium

We calculate the time evolution of a far-from-equilibrium initial state of a non-relativistic ultracold Bose gas in one spatial dimension. The non-perturbative approximation scheme is based on a systematic expansion of the two-particle irreducible effective action in powers of the inverse number of field components. This yields dynamic equations which contain direct scattering, memory and off-shell effects that are not captured in mean-field theory.

cond-mat.other↗

arXiv2003

Pulsed Raman output coupler for an atom laser

We theoretically study a pulsed stimulated two-photon Raman outcoupler for an atom laser using a full three-dimensional description. A finite-temperature trapped Bose-condensed atomic gas is treated self-consistently by the Hartree-Fock-Bogoliubov equations. The model is closely related to a recent experiment on optical outcoupling [E.W. Hagley et al., Science 283, 1706 (1999)]. We analyze the momentum distribution of the output atoms and show how the output beam may be used as a probe of the quantum state for the trapped atomic gas and how it could be engineered and controlled in a nonlinear way.

cond-mat.soft↗

arXiv2002

Exciting Relative Number Squeezed Particles from Condensates Using Stimulated Light Scattering

We investigate the relative particle number squeezing produced in the excited states of a weakly interacting condensate at zero temperature by stimulated light scattering using a pair of lasers. We shall show that a modest number of relative number squeezed particles can be achieved when atoms with momentum $k$, produced in pairs through collisions in the condensate, are scattered out by their interaction with the lasers. This squeezing is optimal when the momentum $k$ is larger than the inverse healing length, $k>k_0$. This modest number of relative number squeezed particles has the potential to be amplified in four-wave-mixing experiments.

quant-ph↗