Three-fluid description of the sympathetic cooling of a boson-fermion mixture

Wouters, Michiel; Tempere, J.; Devreese, Jozef T.

doi:10.1103/physreva.66.043414

Cited by 12 publications

(14 citation statements)

References 9 publications

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“…Various theoretical groups have considered improved cooling schemes [11], including optimizing the evaporation rate [12], using different trapping frequencies [13,14], or using laser rather than evaporative cooling [15,16,17]. We will restrict our investigation to a simple model of sympathetic cooling of a gas in a box, in which it will be shown that a minimum temperature arises naturally as a result of loss of particles.…”

Section: Introductionmentioning

confidence: 99%

Limits of sympathetic cooling of fermions by zero-temperature bosons due to particle losses

Carr

Bourdel

2004

Phys. Rev. A

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It has been suggested by Timmermans [Phys. Rev. Lett. 87, 240403 (2001)] that loss of fermions in a degenerate system causes strong heating. We address the fundamental limit imposed by this loss on the temperature that may be obtained by sympathetic cooling of fermions by bosons. Both a quantum Boltzmann equation and a quantum Boltzmann master equation are used to study the evolution of the occupation number distribution. It is shown that, in the thermodynamic limit, the Fermi gas cools to a minimal temperature kBT /µ ∝ (γ loss /γ coll ) 0.44 , where γ loss is a constant loss rate, γ coll is the bare fermion-boson collision rate not including the reduction due to Fermi statistics, and µ ∼ kBTF is the chemical potential. It is demonstrated that, beyond the thermodynamic limit, the discrete nature of the momentum spectrum of the system can block cooling. The unusual nonthermal nature of the number distribution is illustrated from several points of view: the Fermi surface is distorted, and in the region of zero momentum the number distribution can descend to values significantly less than unity. Our model explicitly depends on a constant evaporation rate, the value of which can strongly affect the minimum temperature.

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Section: Introductionmentioning

confidence: 99%

Limits of sympathetic cooling of fermions by zero-temperature bosons due to particle losses

Carr

Bourdel

2004

Phys. Rev. A

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“…A similar semiclassical and discrete model for sympathetic cooling was put forward in Ref. [13], with the addition of features like collisional losses and spacedependent effects in the evaporation process, but without a determination of the limits of the cooling process. Using our idealized model, we shall then show that the argument based on the heat capacities is approximately correct for fermions cooled by an ideal Boltzmann gas [14], but incorrect when cooled by an ideal Bose gas below the Bose condensation temperature T c .…”

Section: Introductionmentioning

confidence: 99%

“…Shown is the temperature of a degenerate Fermi gas sympathetically cooled by a Bose gas with a condensate present, as a function of the number of bosons evaporated in a harmonic trap, that is, of the difference between the initial number of bosons N b,0 [assumed to fulfill Eqs (13). and(14)] and the final number N b .…”

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confidence: 99%

Limits of sympathetic cooling of fermions: The role of heat capacity of the coolant

Carr

2004

Phys. Rev. A

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The sympathetic cooling of an initially degenerate Fermi gas by either an ideal Bose gas below T c or an ideal Boltzmann gas is investigated. It is shown that the efficiency of cooling by a Bose gas below T c is by no means reduced when its heat capacity becomes much less than that of the Fermi gas, where efficiency is measured by the decrease in the temperature of the Fermi gas per number of particles evaporated from the coolant. This contradicts the intuitive idea that an efficient coolant must have a large heat capacity. In contrast, for a Boltzmann gas a minimal value of the ratio of the heat capacities is indeed necessary to achieve T = 0 and all of the particles must be evaporated.

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“…Sympathetic cooling has been recently considered by several theoretical groups [15][16][17][18][19][20][21][22]. It should be stressed, however, that the limitations due to particle losses have been addressed c EDP Sciences…”

Section: Pacs 0375ss -Degenerate Fermi Gasesmentioning

confidence: 99%

“…In this crossover, which has recently attracted a large attention, strong evidences for superfluidity have been observed [10][11][12][13][14]. Another obstacle appears when a Fermionic gas is sympathetically cooled using a Bose-Einstein condensate, since as a consequence of the superfluid properties of the condensate, the sympathetic cooling is limited to velocities larger than the sound velocity [15].Sympathetic cooling has been recently considered by several theoretical groups [15][16][17][18][19][20][21][22]. It should be stressed, however, that the limitations due to particle losses have been addressed c EDP Sciences…”

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confidence: 99%

Sympathetic cooling of trapped fermions by bosons in the presence of particle losses

2005

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PACS. 03.75.Ss -Degenerate Fermi gases.Abstract. -We study the sympathetic cooling of a trapped Fermi gas interacting with an ideal Bose gas below the critical temperature of the Bose-Einstein condensation. We derive the quantum master equation, which describes the dynamics of the fermionic component, and postulating the thermal distribution for both gases we calculate analytically the rate at which fermions are cooled by the bosonic atoms. The particle losses constitute an important source of heating of the degenerate Fermi gas. We evaluate the rate of loss-induced heating and derive analytical results for the final temperature of fermions, which is limited in the presence of particle losses.Evaporative cooling has proven to be an essential tool to obtain degenerate Fermi gases [1][2][3][4][5][6]. In Fermi systems, the s-wave collisions of indistinguishable particles are forbidden due to the antisymmetry requirement, and therefore the only way to cool fermions using collisions, is to cool them sympathetically by bringing them in contact with atoms in different hyperfine states, or another species. In the regime of quantum degeneracy, however, also the collisional processes in Fermi-Fermi mixtures are strongly suppressed due to Pauli blocking. As a consequence, the efficiency of sympathetic cooling is reduced, and the particle losses, which provide an important source of heating in the degenerate regime [7], prevent from reaching the lower temperatures T, necessary, for instance, for achievement of the superfluid BCS state. This problem may be avoided by adiabatic crossing of a Feshbach resonance, since very low temperatures may be achieved [8] when moving from a molecular BEC regime [9] to the BCS regime. In this crossover, which has recently attracted a large attention, strong evidences for superfluidity have been observed [10][11][12][13][14]. Another obstacle appears when a Fermionic gas is sympathetically cooled using a Bose-Einstein condensate, since as a consequence of the superfluid properties of the condensate, the sympathetic cooling is limited to velocities larger than the sound velocity [15].Sympathetic cooling has been recently considered by several theoretical groups [15][16][17][18][19][20][21][22]. It should be stressed, however, that the limitations due to particle losses have been addressed c EDP Sciences

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Three-fluid description of the sympathetic cooling of a boson-fermion mixture

Cited by 12 publications

References 9 publications

Limits of sympathetic cooling of fermions by zero-temperature bosons due to particle losses

Limits of sympathetic cooling of fermions by zero-temperature bosons due to particle losses

Limits of sympathetic cooling of fermions: The role of heat capacity of the coolant

Sympathetic cooling of trapped fermions by bosons in the presence of particle losses

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