arXiv subjects

Simon A. Gardiner

Publications and source records attributed to Simon A. Gardiner.

27 records · Page 2Linked to original sources

arXiv2015

From short-time diffusive to long-time ballistic dynamics: the unusual center-of-mass motion of quantum bright solitons

Brownian motion is ballistic on short time scales and diffusive on long time scales. Our theoretical investigations indicate that one can observe the exact opposite - an "anomaleous diffusion process" where initially diffusive motion becomes ballistic on longer time scales - in an ultracold atom system with a size comparable to macromolecules. This system is a quantum matter-wave bright soliton subject to decoherence via three-particle losses for which we investigate the center-of-mass motion. Our simulations show that such unusual center-of-mass dynamics should be observable on experimentally accessible time scales.

cond-mat.quant-gas↗

arXiv2013

Phase-matching condition for enhanced entanglement of colliding indistinguishable quantum bright solitons in a harmonic trap

We investigate finite number effects in collisions between two states of an initially well defined number of identical bosons with attractive contact interactions, oscillating in the presence of harmonic confinement in one dimension. We investigate two $N/2$ atom bound states, which are initially displaced (symmetrically) from the trap center, and then left to freely evolve. For sufficiently attractive interactions, these bound states are like those found through use of the Bethe Ansatz (quantum solitons). However, unlike the free case, the integrability is lost due to confinement, and collisions can cause mixing into different bound state configurations. We study the system numerically for the simplest case of $N=4$, via an exact diagonalization of the Hamiltonian within a finite basis, investigating left/right number uncertainty as our primary measure of entanglement. We find that for certain interaction strengths, a phase matching condition leads to resonant transfer to different bound state configurations with highly non-Poissonian relative number statistics.

cond-mat.quant-gas↗

arXiv2013

Tunneling of the 3rd Kind: A Test of the Effective Non-locality of Quantum Field Theory

Integrating out virtual quantum fluctuations in an originally local quantum field theory results in an effective theory which is non-local. In this Letter we argue that tunneling of the 3rd kind - where particles traverse a barrier by splitting into a pair of virtual particles which recombine only after a finite distance - provides a direct test of this non-locality. We sketch a quantum-optical setup to test this effect, and investigate observable effects in a simple toy model.

quant-ph↗

arXiv2013

Collision dynamics and entanglement generation of two initially independent and indistinguishable boson pairs in one-dimensional harmonic confinement

We investigate finite number effects in collisions between two states of an initially well known number of identical bosons with contact interactions, oscillating in the presence of harmonic confinement in one dimension. We investigate two N/2 (interacting) ground states, which are initially displaced from the trap center, and the effects of varying interaction strength. The numerics focus on the simplest case of N=4. In the non-interacting case, such a system would display periodic oscillation with a half harmonic oscillator period (due to the left-right symmetry). With the addition contact interactions between the bosons, collisions generate entanglement between each of the states and distribute energy into other modes of the oscillator. We study the system numerically via an exact diagonalization of the Hamiltonian with a finite basis, investigating left/right number uncertainty as our primary measure of entanglement. Additionally we study the time-evolution and equilibration of the single-body von Neumann entropy for both the attractive and repulsive cases. We identify parameter regimes for which attractive interactions create qualitatively different behavior to repulsive interactions, due to the presence of bound states (quantum solitons) and explain the processes behind this.

cond-mat.quant-gas↗

arXiv2012

Quantum theory of bright matter wave solitons in harmonic confinement

This paper investigates bright quantum-matter-wave solitons beyond the Gross-Pitaevskii equation (GPE). As proposals for interferometry and creating nonlocal quantum superpositions have been formed, it has become necessary to investigate effects not present in mean-field models. We investigate the effect of harmonic confinement on the internal degrees of freedom, as the ratio of zero-point harmonic oscillator length to classical soliton length, for different numbers of atoms. We derive a first-order energy correction for the addition of a harmonic potential to the many-body wave function and use this to create a variational technique based on energy minimization of this wave function for an arbitrary number of atoms, and include numerics based on diagonalization of the Hamiltonian in a basis of harmonic oscillator Fock states. Finally we compare agreement between a Hartree product ground state and the Bethe ansatz solution with a Gaussian envelope localizing the center of mass and show a region of good agreement.

cond-mat.quant-gas↗

arXiv2012

Bright matter-wave soliton collisions at narrow barriers

We study fast-moving bright solitons in the focusing nonlinear Schrödinger equation perturbed by a narrow Gaussian potential barrier. In particular, we present a general and comprehensive analysis of the case where two fast-moving bright solitons collide at the location of the barrier. In the limiting case of a delta-function barrier, we use a quasi-analytic method to show that the relative norms of the outgoing waves depends sinusoidally on the relative phase of the incoming waves, and to determine whether one, or both, of the outgoing waves are bright solitons. We show using numerical simulations that this quasi-analytic result is valid in the high velocity limit: outside this limit nonlinear effects introduce a skew to the phase-dependence, which we quantify. Finally, we numerically explore the effects of introducing a finite-width Gaussian barrier. Our results are particularly relevant, as they can be used to describe a range of interferometry experiments using bright solitary matter-waves.

cond-mat.quant-gas↗

arXiv2004

Adiabatic association of ultracold molecules via magnetic field tunable interactions

We consider in detail the situation of applying a time dependent external magnetic field to a 87Rb atomic Bose-Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of T. Koehler and K. Burnett [Phys. Rev. A 65, 033601 (2002)] to study the efficiency of the association of molecules in a 87Rb Bose-Einstein condensate during a linear passage of the magnetic field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau-Zener, configuration interaction, and two level mean field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose-Einstein condensed gas, provided that the magnetic field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic field strength, and identify the Landau-Zener coefficient determined by F.H. Mies et al. [Phys. Rev. A 61, 022721 (2000)] as the main parameter that controls the efficiency.

cond-mat↗

arXiv2003

Decoherence of Bose-Einstein condensates in microtraps

We discuss the impact of thermally excited near fields on the coherent expansion of a condensate in a miniaturized electromagnetic trap. Monte Carlo simulations are compared with a kinetic two-component theory and indicate that atom interactions can slow down decoherence. This is explained by a simple theory in terms of the condensate dynamic structure factor.

cond-mat.soft↗

arXiv2002

Quantum field theory of dilute homogeneous Bose-Fermi-mixtures at zero temperature: general formalismand beyond mean-field corrections

We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green's functions. We introduce a new relevant object, the renormalized boson-fermion T-matrix which we determine to second order in the boson-fermion s-wave scattering length. We also discuss how to incorporate the usual boson-boson T-matrix in mean-field approximation to obtain the total ground state properties of the system. The next order term beyond mean-field stems from the boson-fermion interaction and is proportional to $a_{\scriptsize BF}k_{\scriptsize F}$. The total ground-state energy-density reads $E/V = ε_{\scriptsize F} + ε_{\scriptsize B} + (2π\hbar^{2}a_{\rm BF}n_{\scriptsize B}n_{\scriptsize F}/m) [1 + a_{\scriptsize BF}k_{\scriptsize F}f(δ)/π]$. The first term is the kinetic energy of the free fermions, the second term is the boson-boson mean-field interaction, the pre-factor to the additional term is the usual mean-field contribution to the boson-fermion interaction energy, and the second term in the square brackets is the second-order correction, where $f(δ)$ is a known function of $δ= (m_{\scriptsize B} - m_{\scriptsize F})/(m_{\scriptsize B} + m_{\scriptsize F})$. We discuss the relevance of this new term, how it can be incorporated into existing theories of boson-fermion mixtures, and its importance in various parameter regimes, in particular considering mixtures of $^{6}$Li and $^{7}$Li and of $^{3}$He and $^{4}$He.

cond-mat↗