M. Olshanii [Phys. Rev. Lett. 81, 938 (1998)] recently solved the atom-atom scattering problem with a pseudopotential interaction in the presence of transverse harmonic confinement, i.e. within an 'atom waveguide', deriving an effective one-dimensional coupling constant that diverged at a "confinement induced resonance" (CIR). Here, we report numerical results for finite range potentials that corroborate this resonance. In addition, we now present a physical interpretation of this effect as a novel type of Feshbach resonance in which the transverse modes of the waveguide assume the roles of 'open' and 'closed' scattering channels. [1,2,3,4,5,6,7,8]. One goal of such experiments is to reach the 'single-mode' or quasi-1D regime, where only the ground state of transverse motion is significantly populated at thermal equilibrium. This regime is of great practical interest due to the potential for ultra-sensitive rotation and gravitational gradient detection with guided single-mode atom interferometers. In addition to such applications, reaching the quasi-1D regime is of significant theoretical interest as the 1D delta-interacting boson gas represents one of the few known fully integrable quantum field theories. In a finite system with infinitely strong (hard-core) deltafunction interactions, boson many-body states in 1D have been shown to correspond via a one-to-one mapping with the highly-correlated states of the corresponding noninteracting Fermi gas [9]. The properties of this TonksGirardeau gas have been a topic of significant current theoretical interest [9,10,11,12,13,14,15] in anticipation of future atom-waveguide experiments. Additionally, the homogeneous 1D Bose with arbitrary-strength delta-function interactions, known as the Lieb Liniger model, is also a fully integrable system [16].To make the connection between experiments in tightly confining waveguides and theoretical models in 1D, it is necessary to know the relationship between the effective 1D coupling constant, g 1D , and the 3D scattering length, a. This problem was first addressed rigorously in [22], where it was predicted that a 'confinement induced resonance' (CIR) modifies the effective interaction, resulting in an effective 1D coupling strength which can be tuned from −∞ to +∞ by varying the transverse width of the * Electronic address: thbergeman@notes.cc.sunysb.edu † Electronic address: mmoore@cfa.harvard.edu ‡ Electronic address: olshanii@phys4adm.usc.edu waveguide, a ⊥ over a small range in the vicinity of the resonance at a ⊥ = Ca, where C = 1.4603 . . .. Hence this resonance clearly has significant implications for atomwaveguide experiments. Until now, however, there has been no convincing physical explanation for the effect, thus raising questions concerning its appearance in systems with finite-range interactions.The primary goal of this Letter, therefore, is to present numerical calculations of scattering in the presence of a cylindrical harmonic potential using finite-range atomatom potentials, confirming the existence of the CIR. ...
In a recent MIT experiment, a new form of superradiant Rayleigh scattering was observed in Bose-Einstein condensates. We present a detailed theory of this phenomena in which condensate depeletion leads to mode competition, which, together with the directional dependence of the scattering rate, is ultimately responsible for the observed phenomena. The nonlinear response of the system is shown to be highly sensitive to initial quantum fluctuations which cause large run to run variations in the observed superradiant pulses.PACS numbers: 03.75.Fi,42.50.Fx With the recent advent of Bose-Einstein condensation (BEC) in low-density alkali vapors [1,2], a laser-like source of coherent monochromatic atomic matter-waves is now readily available. As the electromagnetic vacuum itself provides a nonlinear medium for atomic fields, an atomic BEC is thus an ideal system to study nonlinear wave-mixing and related phenomena. Indeed, nonlinear atom optics [3-5] is now an experimental reality with the recent observation of atomic four-wave mixing in condensate systems [6,7]. In addition to wave-mixing between atomic matter waves, the ability to generate laser-like atomic fields also raises the possibility to observe direct wave-mixing between atomic and optical fields.In the case where the atoms interact only with far off-resonant optical fields, the dominant atom-photon interaction is two-photon Rayleigh scattering. When the atoms are described as matter waves, Rayleigh scattering is formally equivalent to a cubic nonlinearity, and therefore leads to four-wave mixing between atomic and optical fields. In recent work [8-10] along these lines, the scattering of light by a condensate from a strong pump laser into a weak quantized optical cavity mode was considered. This work was an extension of the collective atomic recoil laser (CARL) [11,12] into the regime of BEC, and focused on exploiting an instability in the lightmatter interaction to parametrically amplify atomic and optical waves as well as to optically manipulate matterwave coherence properties and generate entanglement between atomic and optical fields. Recent experiments by Ketterle and coworkers ar MIT[13], however, have demonstrated that this instability can play an important role also in the case in which laser light is scattered into the vacuum modes of the electromagnetic field. In these experiments, a variation of Dicke superradiance [14] was observed in which the role of electronic coherence, which stores the memory of previous scattering events, is replaced by coherence between center-of-mass momentum states, i.e. interference fringes in the atomic density. In this paper we present a multi-mode theory of condensate superradiance. Beginning with the elimination of the radiated light field as in the Wigner-Weiskopf theory of spontaneous emission, we then derive a linearized model which describes amplification of quantum fluctuations. This is then coupled to a 'classical' nonlinear model in which mode competition quenches scattering in all but the direction(s) of ma...
We study the possibility of creating many-particle macroscopic quantum superposition ͑Schrödinger cat͒like states by using a Feshbach resonance to reverse the sign of the scattering length of a Bose-Einstein condensate trapped in a double-well potential. To address the issue of the experimental verification of coherence in the catlike state, we study the revival of the initial condensate state in the presence of environmentally induced decoherence. As a source of decoherence, we consider the interaction between the atoms and the electromagnetic vacuum, due to the polarization induced by an incident laser field. We find that the resulting decoherence is directly related to the rate at which spontaneously scattered photons carry away sufficient information to distinguish between the two atom distributions which make-up the cat state. We show that for a "perfect" cat state, a single scattered photon will bring about a collapse of the superposition, while a less-than-perfect catlike state can survive multiple scatterings before the collapse occurs. In addition, we study the dephasing effect of atom-atom collisions on the catlike states.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.