Excitation Spectrum of a Bose-Einstein Condensate

Steinhauer, Jeff; Ozeri, Roee; Katz, Nadav; Davidson, Nir

doi:10.1103/physrevlett.88.120407

Cited by 350 publications

(424 citation statements)

References 24 publications

(51 reference statements)

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“…[5][6][7][8] Still, the most convincing demonstration of superfluidity remains the measurement of the excitation spectrum of the Bose gas. This spectrum should not only show a phononlike behavior 9,10 but also the appearance of a negative energy dispersion, often called "ghost branch," resulting from the prevalence of parametric processes in the excitation of the quantum fluid. 11 Such a negative energy resonance has been first observed by Vogels et al with condensates of sodium atoms in a magnetic trap.…”

Section: Introductionmentioning

confidence: 99%

Four-wave mixing excitations in a dissipative polariton quantum fluid

et al. 2012

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The Bogoliubov transformation of a polariton quantum fluid has recently been revealed in the four-wave mixing response of a driven microcavity polariton gas. In this work, we investigate the modifications that the dual nature of microcavity polaritons produce on the excitations of this particular half-light-half-matter quantum fluid. We discuss in particular the Bogoliubov character of the excitations of a lower polariton superfluid when it coexists with upper polaritons. We show unique effects resulting from the interplay between polariton decay and Bogoliubov transformation such as the modification of the Bogoliubov dispersion or the slowing down of the four-wave mixing dynamics.

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Section: Introductionmentioning

confidence: 99%

Four-wave mixing excitations in a dissipative polariton quantum fluid

et al. 2012

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“…For the same reasons that polaritons benefit from unusually favourable features for condensation, such as very high critical temperatures, it is expected that their superfluid properties would likewise manifest with altogether different magnitudes, such as very high critical velocities. Since they have shown many deviations in their Bose-condensed phase from the cold atoms paradigm, it is not clear a priori to which extent their superfluid properties would coincide or depart from those observed with atoms, among which quantised vortices 6 , frictionless motion 7 , linear dispersion for the elementary excitations 8 , or more recently Čerenkov emission of a condensate flowing at supersonic velocities 9 , are among the clearest signatures of quantum fluid propagation.…”

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confidence: 99%

Collective fluid dynamics of a polariton condensate in a semiconductor microcavity

Amo¹,

Sanvitto²,

Laussy

et al. 2009

Nature

551

538

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Below a critical temperature, a sufficiently high density of bosons undergoes Bose-Einstein condensation (BEC). Under this condition, the particles collapse into a macroscopic condensate with a common phase, showing collective quantum behaviour like superfluidity, quantised vortices, interferences, etc. Up to recently, BEC was only observed for diluted atomic gases at μK temperatures. Following the recent observations of non-equilibrium BEC in semiconductor microcavities at temperatures of ~10 K, using momentum-1 and real-space 2 trapping, the quest is now towards the observation of the superfluid motion of a polariton BEC. For the same reasons that polaritons benefit from unusually favourable features for condensation, such as very high critical temperatures, it is expected that their superfluid properties would likewise manifest with altogether different magnitudes, such as very high critical velocities. Since they have shown many deviations in their Bose-condensed phase from the cold atoms paradigm, it is not clear a priori to which extent their superfluid properties would coincide or depart from those observed with atoms, among which quantised vortices 6 , frictionless motion 7 , linear dispersion for the elementary excitations 8 , or more recently Čerenkov emission of a condensate flowing at supersonic velocities 9 , are among the clearest signatures of quantum fluid propagation.Microcavity polaritons are two-dimensional bosons of mixed electronic and photonic nature, formed by the strong coupling of excitons-confined in semiconductor quantum wells-with photons trapped in a micron scale resonant cavity. First observed in 1992 10 , these particles have been profusely studied in the last fifteen years due to their unique features. Thanks to their photon fraction, polaritons can easily be excited by an external laser source and detected by light emission in the direction perpendicular to the cavity plane. However, as opposed to photons, they experience strong interparticle interactions owing to their partially electronic fraction. Due to the deep polariton dispersion, the effective mass of these particles is 10 4 -10 5 smaller than the free electron mass, resulting in a very low density of states. This allows for a high state 3 occupancy even at relatively low excitation intensities. However, polaritons live only a few 10 -12 s in a cavity before escaping and therefore thermal equilibrium is never achieved. In this respect, a macroscopically degenerate state of polaritons departs strongly from an atomic Bose-condensed phase. The experimental observations of spectral and momentum narrowing, spatial coherence and long range order-which have been used as evidence for polariton Bose-Einstein condensation-are also present in a pure photonic laser 11 . The recent observation of long range spatial coherence 12 , vortices 4 and the loss of coherence with increasing density in the condensed phase 13,14 , are in accordance with macroscopic phenomena proper of interacting, coherent bosons 15 . But a direct manifestation ...

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“…Interesting phenomena occur also for low optical potential depth, for instance Bloch oscillations [4] and tunneling effects [5][6][7] can be investigated in this regime. In 1D optical lattices the transition to the insulator phase is expected to take place for very large intensities of the optical lattice, so that there is a very extended range of parameters where the gas can be described as a fully coherent system.In this Letter, we study the elementary excitations of an interacting Bose gas in the presence of a periodic potential and discuss how these states can be excited via inelastic processes using, for example, Bragg spectroscopy [8,9]. To this purpose we develop the formalism of the dynamic structure factor, a quantity directly related to the linear response of the system.…”

mentioning

confidence: 99%

“…In this Letter, we study the elementary excitations of an interacting Bose gas in the presence of a periodic potential and discuss how these states can be excited via inelastic processes using, for example, Bragg spectroscopy [8,9]. To this purpose we develop the formalism of the dynamic structure factor, a quantity directly related to the linear response of the system.…”

mentioning

confidence: 99%

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Dynamic structure factor of a Bose-Einstein condensate in a one-dimensional optical lattice

et al. 2003

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We study the effect of a one dimensional periodic potential on the dynamic structure factor of an interacting Bose Einstein condensate at zero temperature. We show that, due to phononic correlations, the excitation strength towards the first band develops a typical oscillating behaviour as a function of the momentum transfer, and vanishes at even multiples of the Bragg momentum. The effects of interactions on the static structure factor are found to be significantly amplified by the presence of the optical potential. Our predictions can be tested in stimulated photon scattering experiments.When a Bose-Einstein condensate is loaded into an optical lattice, its properties change in a very strong way [1]. For deep potential wells, it even happens that the coherence of the sample is lost and one observes the transition to the Mott-insulator phase [2,3]. Interesting phenomena occur also for low optical potential depth, for instance Bloch oscillations [4] and tunneling effects [5][6][7] can be investigated in this regime. In 1D optical lattices the transition to the insulator phase is expected to take place for very large intensities of the optical lattice, so that there is a very extended range of parameters where the gas can be described as a fully coherent system.In this Letter, we study the elementary excitations of an interacting Bose gas in the presence of a periodic potential and discuss how these states can be excited via inelastic processes using, for example, Bragg spectroscopy [8,9]. To this purpose we develop the formalism of the dynamic structure factor, a quantity directly related to the linear response of the system. We will restrict ourselves to the case of a system in the presence of a 1-dimensional optical potentialcreated by two counterpropagating laser beams. In Eq.(1) d is the lattice spacing and s is a dimensionless parameter which denotes the intensity of the laser in units of the recoil energy E R = q 2 B /2m. Here q B =hπ/d is the Bragg momentum denoting the boundary of the first Brillouin zone and m is the atomic mass. The inclusion of an additional harmonic potential produced, for example, by magnetic trapping does not modify the excitation spectrum in a profound way, unless the wave length of the excitation is comparable with the size of the sample. Along the tranverse directions we assume uniform confinement, so that the 3D Gross-Pitaevkii (GP) equation for the ground state order parameter ϕ(z) takes the 1D formwhere n is the average 3D density and the order parameter ϕ is normalized according to d/2 −d/2 |ϕ(z)| 2 dz = 1. As usual g = 4πh 2 a/m is the interaction coupling constant fixed by the scattering length a.The elementary excitations correspond to the solutions of the linearized time-dependent GP-equation and are described by the Bogoliubov equationswhere ϕ is the ground state solution of Eq.(2) and the amplitudes u jq and v jq satisfy the normalization conditionThe solutions u jq (z) and v jq (z) are Bloch waves: u jq (z) = exp(iqz/h)ũ jq (z) whereũ jq is periodic in space with peri...

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Excitation Spectrum of a Bose-Einstein Condensate

Cited by 350 publications

References 24 publications

Four-wave mixing excitations in a dissipative polariton quantum fluid

Four-wave mixing excitations in a dissipative polariton quantum fluid

Collective fluid dynamics of a polariton condensate in a semiconductor microcavity

Dynamic structure factor of a Bose-Einstein condensate in a one-dimensional optical lattice

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