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arXiv:1008.1831 · Physical Review A

Generation of directional, coherent matter beams through dynamical instabilities in Bose-Einstein condensates

G. R. Dennis, Mattias Johnsson

Published Sep 21, 2010• 8 citations
arXivHTMLPDF

Abstract

We present a theoretical analysis of a coupled, two-state Bose-Einstein condensate with nonequal scattering lengths and show that dynamical instabilities can be excited. We demonstrate that these instabilities are exponentially amplified, resulting in highly directional, oppositely propagating, coherent matter beams at specific momenta. To accomplish this we prove that the mean field of our system is periodic and extend the standard Bogoliubov approach to consider a time-dependent, but cyclic, background. This allows us to use Floquet's theorem to gain analytic insight into such systems, rather than employing the usual Bogoliubov--de Gennes approach, which is usually limited to numerical solutions. We apply our theory to the metastable helium atom laser experiment by Dall et al. [Phys. Rev. A 79, 011601(R) (2009)] and show that it explains the anomalous beam profiles they observed. Finally, we demonstrate that the paired particle beams will be Einstein-Podolsky-Rosen entangled on formation.

DOI
10.1103/physreva.82.033615

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We present a theoretical analysis of a coupled, two-state Bose-Einstein condensate with nonequal scattering lengths and show that dynamical instabilities can be excited. We demonstrate that these instabilities are exponentially amplified, resulting in highly directional, oppositely propagating, coherent matter beams at specific momenta. To accomplish this we prove that the mean field of our system is periodic and extend the standard Bogoliubov approach to consider a time-dependent, but cyclic, background. This allows us to use Floquet's theorem to gain analytic insight into such systems, rather than employing the usual Bogoliubov--de Gennes approach, which is usually limited to numerical solutions. We apply our theory to the metastable helium atom laser experiment by Dall et al. [Phys. Rev. A 79, 011601(R) (2009)] and show that it explains the anomalous beam profiles they observed. Finally, we demonstrate that the paired particle beams will be Einstein-Podolsky-Rosen entangled on formation.
The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a thermal cloud and the dynamical depletion of the condensate. Our numerical results, based on the time-dependent Hartree-Fock-Bogoliubov theory, demonstrate the collapse of the attractively interacting BEC via collisional emission of atom pairs into the thermal cloud, which splits the (quasi-one-dimensional) BEC soliton into two partially coherent solitonic structures of opposite momenta. These incoherent matter waves are analogous to optical random-phase solitons.
Abstract The ability to cool quantum gases into the quantum degenerate realm has opened up possibilities for an extreme level of quantum-state control. In this paper, we investigate one such control protocol that demonstrates the resonant amplification of quasimomentum pairs from a Bose–Einstein condensate by the periodic modulation of the two-body s-wave scattering length. This shows a capability to selectively amplify quantum fluctuations with a predetermined momentum, where the momentum value can be spectroscopically tuned. A classical external field that excites pairs of particles with the same energy but opposite momenta is reminiscent of the coherently-driven nonlinearity in a parametric amplifier crystal in nonlinear optics. For this reason, it may be anticipated that the evolution will generate a ‘squeezed’ matter-wave state in the quasiparticle mode on resonance with the modulation frequency. Our model and analysis is motivated by a recent experiment by Clark et al that observed a time-of-flight pattern similar to an exploding firework (Clark et al 2017 Nature 551 356–9). Since the drive is a highly coherent process, we interpret the observed firework patterns as arising from a monotonic growth in the two-body correlation amplitude, so that the jets should contain correlated atom pairs with nearly equal and opposite momenta. We propose a potential future experiment based on applying Ramsey interferometry to experimentally probe these pair correlations.
Summary form only given. Bose-Einstein condensed atomic gases are a new class of quantum fluids with many novel properties. We have studied collective modes and dissipation by perturbing the condensate with focused laser beams. The scattering of photons imparts momentum to the condensate and creates excitations. Consequently, the coherence and collective behavior of the condensate can strongly affect optical properties. We used light scattering to demonstrate that the coherence length of a condensate is equal to its physical size, and obtained dramatic evidence for the presence of correlated momentum excitations in the many-body condensate wavefunction. At higher laser intensity, a new form of superradiance was found which provided a gain mechanism for the generation of directed beams of atoms and light. This process amplified matter waves in a phase coherent way.
Emission of matter wave jets has been recently observed in a Bose-Einstein condensate confined by a cylindrical box potential, induced by a periodically modulated inter-particle interaction (Nature {\bf 551}, 356 (2017)). In this letter we apply the number-conserving time-dependent Bogoliubov theory to study the highly non-equilibrium quantum dynamics in this system. Without any fitting parameter, our theoretical calculations on the dynamics of the jet emission and the angular density correlation are in excellent quantitative agreement with the experimental measurements. In particular, our theory interprets the angular density correlation of the jets as the Hanbury-Brown-Twiss effect between the excited quasi-particles with different angular momenta, and this explains the puzzling observation of the asymmetric density correlations between the jets with the same and opposite momenta. We also analytically show that the number of atoms in the jet emission increases quadratically at early times and is followed by an exponential growth at later times.
In this paper, we examine the possibility of generating bright and dark solitons, as well as multi-pulse solitary waves in Bose–Einstein condensates. Starting from the linear limit of the problem, where such solutions are known explicitly , we use 'dynamic continuation' through the temporal variation of the scattering length, which can be realized in experiments upon using external time-dependent magnetic fields. We examine the stability of the resulting solutions both through direct numerical simulations and through numerical continuation of the relevant steady states and linear stability analysis. Analytical results, illustrating the nature of the bifurcation of the nonlinear solutions, are found to be in good agreement with the numerical findings.
We consider the interaction between a Bose-Einstein condensate and a single-mode quantized light field in the presence of a strong far-off-resonant pump laser. The dynamics is characterized by an exponential instability, hence the system acts as an atom-photon parametric amplifier. Triggered by a small injected probe field, or simply by quantum noise, entangled atom-photon pairs are created which exhibit nonclassical correlations similar to those seen between photons in the optical parametric amplifier. In addition, the quantum statistics of the matter and light field depend strongly on the initial state which triggers the amplifier. Thus, by preparing different initial states of the light field, one can generate matter waves in a variety of quantum states, demonstrating optical control over the quantum statistics of matter waves.