Conditions for Bose-Einstein condensation in magnetically trapped atomic cesium

Tiesinga, Eite; Moerdijk, A. J.; Verhaar, B.J.; Stoof, H. T. C.

doi:10.1103/physreva.46.r1167

Cited by 216 publications

(168 citation statements)

References 14 publications

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“…Under most circumstances, a is insensitive to external fields. This is different in the vicinity of a so-called Feshbach resonance, where a can be tuned over a huge range by adjusting the externally applied magnetic field 4,5 . This has been demonstrated in recent years with cold 85 Rb and Cs atoms 6,7,8 , and with Na and 85 Rb BoseEinstein condensates 9,10 .…”

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confidence: 99%

Dynamics of collapsing and exploding Bose–Einstein condensates

Donley

Claussen

Cornish

et al. 2001

Nature

745

909

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We explored the dynamics of how a Bose-Einstein condensate collapses and subsequently explodes when the balance of forces governing the size and shape of the condensate is suddenly altered. A condensate's equilibrium size and shape is strongly affected by the inter-atomic interactions. Our ability to induce a collapse by switching the interactions from repulsive to attractive by tuning an externally-applied magnetic field yields a wealth of detailed information on the violent collapse process. We observe anisotropic atom bursts that explode from the condensate, atoms leaving the condensate in undetected forms, spikes appearing in the condensate wave function, and oscillating remnant condensates that survive the collapse. These all have curious dependencies on time, the strength of the interaction, and the number of condensate atoms. Although ours would seem to be a simple well-characterized system, our measurements reveal many interesting phenomena that challenge theoretical models.Although the density of the atoms in an atomic BoseEinstein condensate (BEC) is typically five orders of magnitude lower than the density of air, the inter-atomic interactions greatly affect a wide variety of BEC properties. These include static properties like the BEC size and shape and the condensate stability, and dynamic properties like the collective excitation spectrum and soliton and vortex behavior. Since all of these properties are sensitive to the inter-atomic interactions, they can be quite dramatically affected by tuning the interaction strength and sign.The vast majority of BEC physics is well described by mean-field theory 1 , in which the strength of the interactions depends on the atom density and on one additional parameter called the s-wave scattering length a. a is determined by the atomic species. When a > 0, the interactions are repulsive. In contrast, when a < 0 the interactions are attractive and a BEC tends to contract to minimize its overall energy. In a harmonic trap, the contraction competes with the kinetic zero-point energy, which tends to spread out the condensate. For a strong enough attractive interaction, there is not enough kinetic energy to stabilize the BEC and it is expected to implode. A BEC can avoid implosion only as long as the number of atoms N 0 is less than a critical value given by 2where dimensionless constant k is called the stability coefficient. The precise value of k depends on the aspect ratio of the magnetic trap 3 . a ho is the harmonic oscillator length, which sets the size of the condensate in the ideal-gas (a = 0) limit. Under most circumstances, a is insensitive to external fields. This is different in the vicinity of a so-called Feshbach resonance, where a can be tuned over a huge range by adjusting the externally applied magnetic field 4,5 . This has been demonstrated in recent years with cold 85 Rb and Cs atoms 6,7,8 , and with Na and 85 Rb BoseEinstein condensates 9,10 . For 85 Rb atoms, a is usually negative, but a Feshbach resonance at ∼155 G allows us to tune a by orders ...

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mentioning

confidence: 99%

Dynamics of collapsing and exploding Bose–Einstein condensates

Donley

Claussen

Cornish

et al. 2001

Nature

745

909

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“…For the attractive boson-fermion interactioñ h, several negative values are taken: α ≡ |h|/g = (0 ∼ 3). It should be noted that the interaction strength can be shifted using the Feshbach resonance phenomena [18], whose applications for K-atom have been discussed in [16,19].…”

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Induced instability for boson-fermion mixed condensates of alkali-metal atoms due to the attractive boson-fermion interaction

2001

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Instabilities for boson-fermion mixed condensates of trapped Alkali atoms due to the bosonfermion attractive interaction are studied using a variational method. Three regions are shown for their instabilities according to the boson-fermion interaction strength: stable, meta-stable and unstable ones. The stability condition is obtained analytically from the asymptotic expansion of the variational total energy. The life-time of metastable states is discussed for tunneling decay, and is estimated to be very long. It suggests that, except near the unstable border, meta-stable mixed condensate should be almost-stable against clusterizations. The critical border between meta-stable and unstable phases is calculated numerically and is shown to be consistent with the Mølmer scaling condition. [5][6][7], dynamical expansions after the removal of trapping potentials [8], and the instability changes of 7 Li-6 Li system with attractive boson-boson interaction [10]. Discoveries of theIn this paper, we study the instabilities and collapses of the polarized boson-fermion mixed condensates due to the attractive boson-fermion interaction. In BEC, such instabilities are observed in several systems: 1) the trapped meta-stable 7 Li BEC (observed experimentally [11]) equilibrated between the attractive boson-boson interaction and the kinetic pressure due to the finite confinement [12], 2) two-component uniform BEC (from bosons 1 and 2), whose stability condition is given by g 11 g 22 > g 2 12 (g ij : the coupling constant between bosons i and j). In the latter case, the stability condition depends only on the interaction strength, but the condition for the case 1) has also the particle number dependence [12].Let us consider the case of the trapped boson-fermion mixed condensate. In the present paper, we assume T = 0 and a spherical harmonic-oscillator for the trapping potential; extension to the deformed potential is straightforward. Using the Thomas-Fermi approximation for the fermion degree of freedom (appropriate for large N f condensate), the total energy of the system becomes a functional of the boson order-parameter Φ( r) and the fermion density distribution n f ( r): (1), the fermion-fermion interaction has been neglected; the elastic fermion-fermion s-wave scattering for a polarized gas is absent because of the Pauli blocking effects and the p-wave scattering is suppressed below 100 µK [14]. Evaluating the total energy with the variational method, we take the Gaussian ansatz for the boson order-parameter:where x = r/ξ is a radial distance scaled by the harmonic-oscillator length ξ = (h/mω) 1/2 , and N b = d 3 x|Φ(x; R)| 2 is total boson number. The variational parameter R in (2) corresponds to the root-mean-square (rms) radius of the boson density distribution. This kind of variational functions have also been used in the instability investigations of 1

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“…The results are scalable. Moreover, the magnitude and sign of the values of a s and µ can be easily tuned by Feshbach resonance [4] and by an external field [18], respectively.…”

Section: Simulation Results and Discussionmentioning

confidence: 99%

“…Accordingly, Bose-Einstein condensates created thus far have been very accurately described by the Gross-Pitaevskii theory (see [2] for a review), a meanfield approach. Furthermore, it has been possible to tune the s-wave scattering length a s to essentially any value, positive or negative, by utilizing a magnetic atom-atom Feshbach resonance [4].…”

Section: Introductionmentioning

confidence: 99%

Bose-Einstein condensation of trapped atoms with dipole interactions

Nho

Landau

2005

Phys. Rev. A

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The path integral Monte Carlo method is used to simulate dilute trapped Bose gases and to investigate the equilibrium properties at finite temperatures. The quantum particles have a long-range dipole-dipole interaction and a short-range s-wave interaction. Using an anisotropic pseudopotential for the long-range dipolar interaction and a hard-sphere potential for the short-range s-wave interaction, we calculate the energetics and structural properties as a function of temperature and the number of particles. Also, in order to determine the effects of dipole-dipole forces and the influence of the trapping field on the dipolar condensate, we use two cylindrically symmetric harmonic confinements (a cigar-shaped trap and a disk-shaped trap). We find that the net effect of dipole-dipole interactions is governed by the trapping geometry. For a cigar-shaped trap, the net contribution of dipolar interactions is attractive and the shrinking of the density profiles is observed. For a disk-shaped trap, the net effect of long-range dipolar forces is repulsive and the density profiles expand.

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Conditions for Bose-Einstein condensation in magnetically trapped atomic cesium

Cited by 216 publications

References 14 publications

Dynamics of collapsing and exploding Bose–Einstein condensates

Dynamics of collapsing and exploding Bose–Einstein condensates

Induced instability for boson-fermion mixed condensates of alkali-metal atoms due to the attractive boson-fermion interaction

Bose-Einstein condensation of trapped atoms with dipole interactions

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