Single Condensate Research Articles

Analytical method for yrast line states in the interacting two-component Bose-Einstein condensate

The yrast spectrum for the harmonically trapped two-component Bose-Einstein condensate (BEC), omitting the difference between the two components, has been studied using an analytical method. The energy eigenstates and eigenvalues for L = 0, 1, 2, 3 are given. We illustrate that there are different eigenstate behaviours between the even L and odd L cases for the two-component BEC in two dimensions. Except for symmetric states, there are antisymmetric states for the permutation of the two components, which cannot reduce to those in a single condensate case when the value of L is odd.

Macroscopic quantum-state reduction: Uniting Bose-Einstein condensates by interference measurements

Two independently prepared condensates can be combined into a single larger condensate by detection of their relative phase in an intereference measurement.

CP and flavour in effective type I string models

Effective type I string models allow stabilization of the dilaton and moduli fields with only a single gaugino condensate. We show that, as well as breaking supersymmetry, the stabilization can spontaneously break CP. We find that this source of CP violation hints strongly at a natural solution to the supersymmetric CP and flavour problems. Even though the CP violation generates physical phases in the Yukawa couplings, all the supersymmetry-breaking terms are found to be automatically real and given by the U(1) charges of the associated Yukawa couplings. These can be chosen to have a structure (degenerate or non-universal) which suppresses FCNCs and EDMs. We examine the phenomenological implications, including the generation of the μ-term, and the effect of higher-order terms.

Researchers Can Now Vary the Atomic Interactions in a Bose–Einstein Condensate

Bose–Einstein condensates (BECs) were formed five years ago from rubidium-87 and sodium atoms, whose interactions are repulsive. BECs were also formed from lithium-7 atoms, which attract one another. (See the article by Wolfgang Ketterle in PHYSICS TODAY, December 1999, page 30.) Now researchers in Boulder, Colorado, have created a single condensate of rubidium-85 atoms, which can be taken continuously from the repulsive to the attractive regimes. The experimenters can vary the strength of the interaction between the atoms in their condensate by a factor of 100 or more—and even flip its sign—by changing the external magnetic field. The ability to tune the interactions of a condensate opens the door to systematic explorations of atomic behavior in new regimes.

Fragmented and single condensate ground states of spin-1 bose Gas

We show that the ground state of a spin-1 Bose gas with an antiferromagnetic interaction is a fragmented condensate in uniform magnetic fields. The number fluctuations in each spin component change rapidly from being enormous (order N) to exceedingly small (order 1) as the magnetization of the system increases. A fragmented condensate can be turned into a single condensate state by magnetic field gradients. The conditions for existence and method of detecting fragmented states are presented.

Feshbach resonances in atomic Bose–Einstein condensates

The low-energy Feshbach resonances recently observed in the inter-particle interactions of trapped ultra-cold atoms involve an intermediate quasi-bound molecule with a spin arrangement that differs from the trapped atom spins. Variations of the strength of an external magnetic field then alter the difference of the initial and intermediate state energies (i.e. the ‘detuning’). The effective scattering length that describes the low-energy binary collisions, similarly varies with the near-resonant magnetic field. Since the properties of the dilute atomic Bose–Einstein condensates (BECs) are extremely sensitive to the value of the scattering length, a ‘tunable’ scattering length suggests very interesting many-body studies. In this paper, we review the theory of the binary collision Feshbach resonances, and we discuss their effects on the many-body physics of the condensate. We point out that the Feshbach resonance physics in a condensate can be considerably richer than that of an altered scattering length: the Feshbach resonant atom–molecule coupling can create a second condensate component of molecules that coexists with the atomic condensate. Far off-resonance, a stationary condensate does behave as a single condensate with effective binary collision scattering length. However, even in the off-resonant limit, the dynamical response of the condensate mixture to a sudden change in the external magnetic field carries the signature of the molecular condensate's presence: experimentally observable oscillations of the number of atoms and molecules. We also discuss the stationary states of the near-resonant condensate system. We point out that the physics of a condensate that is adiabatically tuned through resonance depends on its history, i.e. whether the condensate starts out above or below resonance. Furthermore, we show that the density dependence of the many-body ground-state energy suggests the possibility of creating a dilute condensate system with the liquid-like property of a self-determined density.

Spatial fragmentation of a Bose-Einstein condensate in a double-well potential

We present a theoretical study of the ground state of a Bose-Einstein condensate with repulsive inter-particle interactions in a double-well potential, using a restricted variational principle. Within such an approach, there is a transition from a single condensate to a fragmented condensate as the strength of the central barrier of the potential is increased. We determine the nature of this transition through approximate analytic as well as numerical solutions of our model in the regime where the inter-particle interactions can be treated perturbatively. The degree of fragmentation of the condensate is characterized by the degrees of first-order and second-order spatial coherence across the barrier.

Dynamical quantum noise in trapped Bose-Einstein condensates

We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-$P$ and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-$P$ approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial state for the condensate and compare results to those for single-mode models.

Quantum state of a trapped Bose-Einstein condensate

The quantum state of a single symmetry-broken condensate at zero temperature is calculated using perturbative techniques. For a fixed mean number of atoms, the state is found to closely approximate a number squeezed state. We propose a means of experimentally testing this state, based on the periodic collapses and revivals of its phase.

Hartree-Fock treatment of the two-component Bose-Einstein condensate

We present a numerical study of a trapped binary Bose-condensed gas by solving the corresponding Hartree-Fock equations. The density profile of the binary Bose gas is solved with a harmonic trapping potential as a function of temperature in two and three dimensions. We find a symmetry breaking in the two dimensional case where the two condensates separate. We also present a phase diagram in the three dimensional case of the different regions where the binary condensate becomes a single condensate and eventually an ordinary gas as function of temperature and the interaction strength between the atoms.

Spontaneous photon emission stimulated by two Bose-Einstein condensates

We show that the phase difference of two overlapping ground state Bose-Einstein condensates can effect the optical spontaneous emission rate of excited atoms. Depending on the phase difference the atom stimulated spontaneous emission rate can vary between zero and the rate corresponding to all the ground state atoms in a single condensate. Besides giving control over spontaneous emission this provides an optical method for detecting the condensate phase difference. It differs from previous methods in that no light fields are applied. Instead the light is spontaneously emitted when excited atoms make a transition into either condensate.

Dilaton stabilization in the context of dynamical supersymmetry breaking through gaugino condensation

We study gaugino condensation in the context of superstring effective theories using the linear multiplet formulation for the dilaton superfield. Including non-perturbative corrections to the Kähler potential for the dilaton may naturally achieve dilaton stabilization, with supersymmetry breaking and gaugino condensation; these three issues are interrelated in a very simple way. In a toy model with a single static condensate, a dilaton vev is found within a phenomenologically interesting range. The effective theory differs significantly from condensate models studied previously in the chiral formulation.

Dilaton stabilization in the context of dynamical supersymmetry breaking through gaugino condensation

We study gaugino condensation in the context of superstring effective theories using the linear multiplet formulation for the dilaton superfield. Including non-perturbative corrections to the Kähler potential for the dilaton may naturally achieve dilaton stabilization, with supersymmetry breaking and gaugino condensation; these three issues are interrelated in a very simple way. In a toy model with a single static condensate, a dilaton vev is found within a phenomenologically interesting range. The effective theory differs significantly from condensate models studied previously in the chiral formulation.

The role of vortex strings in the non-compact lattice Abelian Higgs model

The non-compact lattice version of the Abelian Higgs model is studied in terms of its topological excitations. The Villain form of the partition function is represented as a sum over world-sheets of gauge-invariant “vortex” strings. The phase transition of the system is then related to the density of these excitations. Through Monte Carlo simulations the density of the vortex sheets is shown to be a good order parameter for the system. The vortex density essentially vanishes in the Higgs phase, and the Coulomb phase consists of a single vortex condensate.

Gaugino condensation, S-duality and supersymmetry breaking in supergravity models

The status of the gaugino condensation as the source of supersymmetry breaking is reexamined. It is argued that one cannot have stable minima with broken supersymmetry in models where the dilaton is coupled only linearly to the gaugino condensate. We show that the problems of the gaugino condensate mechanism can be solved by considering non-standard gauge kinetic functions, created by non-perturbative effects. As an example we use the principle of S-duality to modify the coupling of the gaugino condensate to effective supergravity (superstring) Lagrangians. We show that such an approach can solve the problem of the runaway dilaton and lead to satisfactory supersymmetry breaking in models with a single gaugino condensate. We exhibit a general property of theories containing a symmetry acting on the dilaton and also shed some light on the question whether it is generically the auxiliary field of the modulus T that dominates supersymmetry breaking.

S-dual gaugino condensation and supersymmetry breaking

The principle of S-duality is used to incorporate gaugino condensates into effective supergravity (superstring) Lagrangians. We discuss two implementations of S-duality which differ in the way the coupling constant is transformed. Both solve the problem of the runaway dilaton and lead to satisfactory supersymmetry breaking in models with a single gaugino condensate. The breakdown of supersymmetry is intimately related to a nontrivial transformation of the condensate under T-duality.

Structure of the condensate and some possible ways to observe it

We review some aspects of the experimental consequences both well known and proposed, of the existence of the single particle condensate in liquid helium four. We also extend these considerations briefly to pair correlations which microscopic calculations show to also exist in the fluid.

Transport-induced shifts in condensate dew-point and composition in multicomponent systems with chemical reaction

We present an analysis of partial heterogeneous condensation phenomena in multicomponent reacting systems, including previously neglected chemical element transport considerations. These phenomena, associated with the tendency of the chemical elements to preferentially “segregate” (according to the local temperature and the transport properties of the chemical species containing each element), are found to: (a) systematically “shift” the prevailing dew-point from that predicted purely thermodynamically, (b) systematically alter concentrations in the incipient condensate and (c) even influence the identity of a resulting single component condensate. Several distinct dew-points are shown to exist in such systems (depending upon one's operational definition or method of detection), and, as a result of transport constraints, the “sharp” locus between two chemically distinct condensates is systematically moved to a difference mainstream composition. These novel aspects of partial condensation-chemical vapor deposition (CVD) phenomena in multicomponent, chemically reacting systems are demonstrated using representative calculations and recent experiments on alkali compound condensation from the gaseous products of fossil fuel combustion. However, the phenomena illustrated here are rather general, and can be anticipated in other CVD-systems of technological importance (e.g. in semiconductor processing) by applying the concepts and methods outlined below.