Collective Excitations of a Bose-Einstein Condensate in a Magnetic Trap

Mewes, M.-O.; Andrews, M. R.; Druten, N. J. van; Kurn, D. M.; Durfee, Dallin; Townsend, C. G.; Ketterle, Wolfgang

doi:10.1103/physrevlett.77.988

Cited by 563 publications

(552 citation statements)

References 14 publications

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“…The existence of such modes below the trapping frequency might be a special feature of superfluid hydrodynamics just as the appearance of a second velocity of sound. Indeed, in their early experiments Stamper-Kurn et al [8] used a cigar-shaped harmonic potential with trapping frequency ω 0z /2π = 18.04(1) Hz in axial direction. They observed an out-of-phase oscillation between condensate and thermal cloud of a Bose gas at T = 1µK in the hydrodynamic regime.…”

Section: Eq (5)mentioning

confidence: 99%

Hydrodynamic collective modes for cold trapped gases

Boettcher¹,

Floerchinger²,

Wetterich³

2011

J. Phys. B: At. Mol. Opt. Phys.

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We suggest that collective oscillation frequencies of cold trapped gases can be used to test predictions from quantum many-body physics. Our motivation lies both in rigid experimental tests of theoretical calculations and a possible improvement of measurements of particle number, chemical potential or temperature. We calculate the effects of interaction, dimensionality and thermal fluctuations on the collective modes of a dilute Bose gas in the hydrodynamic limit. The underlying equation of state is provided by non-perturbative Functional Renormalization Group or by LeeYang theory. The spectrum of oscillation frequencies could be measured by response techniques. Our findings are generalized to bosonic or fermionic quantum gases with an arbitrary equation of state in the two-fluid hydrodynamic regime. For any given equation of state P (µ, T ) and normal fluid density nn(µ, T ) the collective oscillation frequencies in a d-dimensional isotropic potential are found to be the eigenvalues of an ordinary differential operator. We suggest a method of numerical solution and discuss the zero-temperature limit. Exact results are provided for harmonic traps and certain special forms of the equation of state. We also present a phenomenological treatment of dissipation effects and discuss the possibility to excite the different eigenmodes individually.

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Section: Eq (5)mentioning

confidence: 99%

Hydrodynamic collective modes for cold trapped gases

Boettcher¹,

Floerchinger²,

Wetterich³

2011

J. Phys. B: At. Mol. Opt. Phys.

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“…These modes have been the object of recent extensive experimental and theoretical work [22][23][24][25]14].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of a trapped Bose-condensed gas

1997

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“…Fi, 05.30.Jp, 67.40.Db In recent experiments on magnetically-trapped atomic vapors, alkali atoms [1][2][3] have been cooled to temperatures at which they are degenerate and indeed BoseEinstein condensation has been observed in them. Frequencies and damping rates of collective modes in these systems have been investigated, both above and below the Bose-Einstein transition temperature, T c [4][5][6]. In this Letter we shall focus on properties above T c .…”

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confidence: 99%

Damping of hydrodynamic modes in a trapped Bose gas above the Bose-Einstein transition temperature

1998

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We calculate the damping of low-lying collective modes of a trapped Bose gas in the hydrodynamic regime, and show that this comes solely from the shear viscosity, since the contributions from bulk viscosity and thermal conduction vanish. The hydrodynamic expression for the damping diverges due to the failure of hydrodynamics in the outer parts of the cloud, and we take this into account by a physically motivated cutoff procedure. Our analysis of available experimental data indicates that higher densities than have yet been achieved are necessary for investigating hydrodynamic modes above the Bose-Einstein transition temperature.PACS numbers: 03.75. Fi, 05.30.Jp, 67.40.Db In recent experiments on magnetically-trapped atomic vapors, alkali atoms [1][2][3] have been cooled to temperatures at which they are degenerate and indeed BoseEinstein condensation has been observed in them. Frequencies and damping rates of collective modes in these systems have been investigated, both above and below the Bose-Einstein transition temperature, T c [4][5][6]. In this Letter we shall focus on properties above T c . One can distinguish two regimes, the hydrodynamic one, for which the characteristic mode frequency is small compared with the collision frequency and the wavelength of the mode is large compared with the atomic mean free path, and the opposite limit, the collisionless one, for which collisions are relatively unimportant. The frequencies of modes in the hydrodynamic regime have been calculated in Ref. [7], and here we calculate their damping.We begin by giving a simple derivation of the basic hydrodynamic equations. Our treatment is essentially that of Ref. [8] generalized to take into account the potential of the trap, and, since we are interested in small oscillations, we shall consider the linearized equations. The Euler equation for the fluid velocity v(r, t) iswhere m is the mass of the atoms, n(r, t) is the particle density, n 0 (r) is the equilibrium particle density, p(r, t) is the pressure and f is the force per unit mass due to the external potential U 0 (r), f = −∇U 0 (r)/m. In equilibrium, where the pressure is p 0 (r), Eq. (1) implies that ∇p 0 (r) = mn 0 (r)f . Taking the time-derivative of Eq.(1) and using the continuity equation, one findsWe calculate the first term on the right hand side of Eq.(2) by using the energy conservation condition [8],where ρ is the mass density and ǫ and w are, respectively, the internal energy and the enthalpy of the fluid per unit mass. Since we assume local thermodynamic equilibrium and neglect contributions to the energy due to interparticle interactions, we may use the results p = ρ(w − ǫ) and ρǫ = 3p/2, and find thatCombining Eqs. (2) and (4), and using the fact that ∇n 0 (r) is proportional to ∇U 0 (r), we obtain for the equation of motion for v(r, t),Equation (5) has previously been derived by Griffin et al.[7] using kinetic theory. In our present discussion we assume that the potential is axially symmetric,where ω 0 is the frequency of the trap in the x − y plane; ...

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Collective Excitations of a Bose-Einstein Condensate in a Magnetic Trap

Cited by 563 publications

References 14 publications

Hydrodynamic collective modes for cold trapped gases

Hydrodynamic collective modes for cold trapped gases

Thermodynamics of a trapped Bose-condensed gas

Damping of hydrodynamic modes in a trapped Bose gas above the Bose-Einstein transition temperature

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