Charles W. Clark

Watching Dark Solitons Decay into Vortex Rings in a Bose-Einstein Condensate

We have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings. We have imaged the resulting vortex rings.

Theory and applications of atomic and ionic polarizabilities

Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability. When it comes to microscopic phenomena, the existence of alkaline-earth anions and the recently discovered ability of positrons to bind to many atoms are predominantly due to the polarization interaction. An imperfect knowledge of atomic polarizabilities is presently looming as the largest source of uncertainty in the new generation of optical frequency standards. Accurate polarizabilities for the group I and II atoms and ions of the periodic table have recently become available by a variety of techniques. These include refined many-body perturbation theory and coupled-cluster calculations sometimes combined with precise experimental data for selected transitions, microwave spectroscopy of Rydberg atoms and ions, refractive index measurements in microwave cavities, ab initio calculations of atomic structures using explicitly correlated wavefunctions, interferometry with atom beams and velocity changes of laser cooled atoms induced by an electric field. This review examines existing theoretical methods of determining atomic and ionic polarizabilities, and discusses their relevance to various applications with particular emphasis on cold-atom physics and the metrology of atomic frequency standards.

Stationary solutions of the one-dimensional nonlinear Schrödinger equation. II. Case of attractive nonlinearity

In this second of two papers, we present all stationary so- lutions of the nonlinear Schrodinger equation with box or pe- riodic boundary conditions for the case of attractive nonlin- earity. The companion paper has treated the case of repulsive nonlinearity. Our solutions take the form of stationary trains of bright solitons. Under box boundary conditions the solu- tions are the bounded analog of bright solitons on the innite line, and are in one-to-one correspondence with particle-in-a- box solutions to the linear Schrodinger equation. Under peri- odic boundary conditions we nd several classes of solutions: constant amplitude solutions corresponding to boosts of the condensate; the nonlinear version of the well-known particle- on-a-ring solutions in linear quantum mechanics; nodeless, real solutions; and a novel class of intrinsically complex, node- less solutions. The set of such solutions on the ring are de- scribed by the Cn character tables from the theory of point groups. We make experimental predictions about the form of the ground state and modulational instability. We show that, though this is the analog of some of the simplest problems in linear quantum mechanics, nonlinearity introduces new and surprising phenomena in the stationary one-dimensional non- linear Schrodinger equation. We also note that in various limits the spectrum of the nonlinear Schrodinger equation re- duces to that of the box, the Rydberg, and the harmonic oscillator, the latter being for repulsive nonlinearity, thus in- cluding the three most common and important cases of linear quantum mechanics.

Collective Excitations of Atomic Bose-Einstein Condensates

We apply linear-response analysis of the Gross-Pitaevskii equation to obtain the excitation frequencies of a Bose-Einstein condensate confined in a time-averaged orbiting potential trap. Our calculated values are in excellent agreement with those observed in a recent experiment.

Quantum key distribution with 1.25 Gbps clock synchronization

Clock recovery techniques at 1.25 Gbps enable continuous quantum key distribution at demonstrated sifted-key rates up to 1.0 Mbps. This rate is two orders of magnitude faster than has been reported previously

Generalized thermalization in an integrable lattice system.

After a quench, observables in an integrable system may not relax to the standard thermal values, but can relax to the ones predicted by the generalized Gibbs ensemble (GGE) [M. Rigol et al., Phys. Rev. Lett. 98, 050405 (2007)]. The GGE has been shown to accurately describe observables in various one-dimensional integrable systems, but the origin of its success is not fully understood. Here we introduce a microcanonical version of the GGE and provide a justification of the GGE based on a generalized interpretation of the eigenstate thermalization hypothesis, which was previously introduced to explain thermalization of nonintegrable systems. We study relaxation after a quench of one-dimensional hard-core bosons in an optical lattice. Exact numerical calculations for up to 10 particles on 50 lattice sites (≈10(10) eigenstates) validate our approach.

Dark-soliton states of Bose-Einstein condensates in anisotropic traps

Dark soliton states of Bose-Einstein condensates in harmonic traps are studied both analytically and computationally by the direct solution of the Gross-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The energy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. Large-amplitude field modulation at a frequency resonant with the energy of a dark soliton is found to give rise to a state with multiple vortices. The Bogoliubov excitation spectrum of the soliton state contains complex frequencies, which disappear for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by propagation in real time.

Hysteresis in a quantized superfluid /`atomtronic/' circuit

Atomtronics is an emerging interdisciplinary field that seeks to develop new functional methods by creating devices and circuits where ultracold atoms, often superfluids, have a role analogous to that of electrons in electronics. Hysteresis is widely used in electronic circuits—it is routinely observed in superconducting circuits and is essential in radio-frequency superconducting quantum interference devices. Furthermore, it is as fundamental to superfluidity (and superconductivity) as quantized persistent currents, critical velocity and Josephson effects. Nevertheless, despite multiple theoretical predictions, hysteresis has not been previously observed in any superfluid, atomic-gas Bose–Einstein condensate. Here we directly detect hysteresis between quantized circulation states in an atomtronic circuit formed from a ring of superfluid Bose–Einstein condensate obstructed by a rotating weak link (a region of low atomic density). This contrasts with previous experiments on superfluid liquid helium where hysteresis was observed directly in systems in which the quantization of flow could not be observed, and indirectly in systems that showed quantized flow. Our techniques allow us to tune the size of the hysteresis loop and to consider the fundamental excitations that accompany hysteresis. The results suggest that the relevant excitations involved in hysteresis are vortices, and indicate that dissipation has an important role in the dynamics. Controlled hysteresis in atomtronic circuits may prove to be a crucial feature for the development of practical devices, just as it has in electronic circuits such as memories, digital noise filters (for example Schmitt triggers) and magnetometers (for example superconducting quantum interference devices).

Observing Zitterbewegung with Ultracold Atoms

We propose an optical lattice scheme which would permit the experimental observation of Zitterbewegung (ZB) with ultracold, neutral atoms. A four-level tripod variant of the setup for stimulated Raman adiabatic passage (STIRAP) has previously been proposed for generating non-Abelian gauge fields. Dirac-like Hamiltonians, which exhibit ZB, are simple examples of such non-Abelian gauge fields; we show how a variety of them can arise, and how ZB can be observed, in a tripod system. We predict that the ZB should occur at experimentally accessible frequencies and amplitudes.

Quantized hysteresis in a superfluid atomtronic circuit

Atomtronics is an emerging interdisciplinary field that seeks to develop new functional methods by creating devices and circuits where ultracold atoms, often superfluids, have a role analogous to that of electrons in electronics. Hysteresis is widely used in electronic circuits—it is routinely observed in superconducting circuits and is essential in radio-frequency superconducting quantum interference devices. Furthermore, it is as fundamental to superfluidity (and superconductivity) as quantized persistent currents, critical velocity and Josephson effects. Nevertheless, despite multiple theoretical predictions, hysteresis has not been previously observed in any superfluid, atomic-gas Bose–Einstein condensate. Here we directly detect hysteresis between quantized circulation states in an atomtronic circuit formed from a ring of superfluid Bose–Einstein condensate obstructed by a rotating weak link (a region of low atomic density). This contrasts with previous experiments on superfluid liquid helium where hysteresis was observed directly in systems in which the quantization of flow could not be observed, and indirectly in systems that showed quantized flow. Our techniques allow us to tune the size of the hysteresis loop and to consider the fundamental excitations that accompany hysteresis. The results suggest that the relevant excitations involved in hysteresis are vortices, and indicate that dissipation has an important role in the dynamics. Controlled hysteresis in atomtronic circuits may prove to be a crucial feature for the development of practical devices, just as it has in electronic circuits such as memories, digital noise filters (for example Schmitt triggers) and magnetometers (for example superconducting quantum interference devices).