Bose-Einstein Condensation in a Gas of Sodium Atoms

Davis, Kendall B.; Mewes, M.-O.; Andrews, M. R.; Druten, N. J. van; Durfee, Dallin; Kurn, D. M.; Ketterle, Wolfgang

doi:10.1109/eqec.1996.561567

Cited by 453 publications

(697 citation statements)

References 2 publications

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“…This result gives the mathematical description of recent experiments (initiated in [7,3]) where the dynamics of Bose-Einstein condensates have been observed.…”

Section: László Erdős Benjamin Schlein and Horng-tzer Yaumentioning

confidence: 99%

Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential

Erdős¹,

Schlein

Yau

2009

J. Amer. Math. Soc.

143

246

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Consider a system of N N bosons in three dimensions interacting via a repulsive short range pair potential N 2 V ( N ( x i − x j ) ) N^2V(N(x_i-x_j)) , where x = ( x 1 , … , x N ) \mathbf {x}=(x_1, \ldots , x_N) denotes the positions of the particles. Let H N H_N denote the Hamiltonian of the system and let ψ N , t \psi _{N,t} be the solution to the Schrödinger equation. Suppose that the initial data ψ N , 0 \psi _{N,0} satisfies the energy condition \[ ⟨ ψ N , 0 , H N ψ N , 0 ⟩ ≤ C N \langle \psi _{N,0}, H_N \psi _{N,0} \rangle \leq C N \] and that the one-particle density matrix converges to a projection as N → ∞ N \to \infty . Then, we prove that the k k -particle density matrices of ψ N , t \psi _{N,t} factorize in the limit N → ∞ N \to \infty . Moreover, the one particle orbital wave function solves the time-dependent Gross-Pitaevskii equation, a cubic nonlinear Schrödinger equation with the coupling constant proportional to the scattering length of the potential V V . In a recent paper, we proved the same statement under the condition that the interaction potential V V is sufficiently small. In the present work we develop a new approach that requires no restriction on the size of the potential.

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“…This result gives the mathematical description of recent experiments (initiated in [7,3]) where the dynamics of Bose-Einstein condensates have been observed.…”

Section: László Erdős Benjamin Schlein and Horng-tzer Yaumentioning

confidence: 99%

Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential

Erdős¹,

Schlein

Yau

2009

J. Amer. Math. Soc.

143

246

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“…For ions, the critical velocity has been observed 10 in superfluid 4 He at the expected value of ≈ 45 m s -1 , and 3 confirmed in superfluid 3 He-B at 28 bar as consistent with the expected ≈ 71 mm s -1 value 11 . For macroscopic objects, the onset of extra dissipation at v L in superfluid 4 He cannot be observed since damping from vorticity becomes prohibitive at much lower velocities. However, while macroscopic objects can be readily accelerated at the lowest temperatures to the much lower critical velocities in superfluid 3 He, the experimental picture is somewhat misleading.…”

mentioning

confidence: 99%

“…For macroscopic objects, the onset of extra dissipation at v L in superfluid 4 He cannot be observed since damping from vorticity becomes prohibitive at much lower velocities. However, while macroscopic objects can be readily accelerated at the lowest temperatures to the much lower critical velocities in superfluid 3 He, the experimental picture is somewhat misleading.…”

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confidence: 99%

Breaking the superfluid speed limit in a fermionic condensate

et al. 2016

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Coherent condensates appear as emergent phenomena in many systems 1-8 , sharing the characteristic feature of an energy gap separating the lowest excitations from the condensate ground state. This implies that a scattering object, moving through the system with high enough velocity for the excitation spectrum in the scatter frame to become gapless, can create excitations at no energy cost, initiating the breakdown of the condensate 1,9-13 . This limit is the well-known Landau velocity 9 . While, for the neutral Fermionic superfluid 3 He-B in the T=0 limit, flow around an oscillating body displays a very clear critical velocity for the onset of dissipation 12,13 , here we show that for uniform linear motion there is no discontinuity whatsoever in the dissipation as the Landau critical velocity is passed and exceeded. Since the Landau velocity is such a pillar of our understanding of superfluidity, this is a considerable surprise, with implications for the understanding of the dissipative effects of moving objects in all coherent condensate systems.The Landau critical velocity marks the minimum velocity at which an object moving through a condensate can generate excitations with zero energy cost 9 . In the frame of the object, moving at velocity v relative to the fluid, excitations of momentum p are shifted, by Galilean transformation, from energy E to (E -v.p). Superfluid 3 He has a BCS dispersion curve 1 with energy minima, E = Δ at momenta ±p F . Therefore excitation generation should begin as soon as one energy minimum reaches zero, i.e. when the velocity reaches the Landau critical value,We can investigate v L in condensates in two limiting regimes, i.e. for the motion of microscopic objects (e.g. ions) or for that of macroscopic objects. For ions, the critical velocity has been observed 10 in superfluid 4 He at the expected value of ≈ 45 m s -1 , and 3 confirmed in superfluid 3 He-B at 28 bar as consistent with the expected ≈ 71 mm s -1 value 11 . For macroscopic objects, the onset of extra dissipation at v L in superfluid 4 He cannot be observed since damping from vorticity becomes prohibitive at much lower velocities. However, while macroscopic objects can be readily accelerated at the lowest temperatures to the much lower critical velocities in superfluid 3 He, the experimental picture is somewhat misleading.In superfluid 3 He, oscillating macroscopic objects do indeed show a sudden increase in damping 12 , but at a velocity of only ≈ v L /3, arising from the emission of quasiparticle excitations from the pumping of surface excitation driven by the reciprocating motion 13 .Although this mechanism does not involve bulk pair breaking, it has created the impression that a Landau critical velocity has indeed been confirmed in 3 He, which is not the case.What should we expect for uniform motion? The textbook prediction suggests that at v L all details of the process become irrelevant. Condensate breakdown becomes inevitable; the constituent Cooper pairs separate; and the properties rapidly approaching those of...

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“…For a gas of atoms confined in an external potential, the quantum statistical properties of the atoms become important at ultralow temperatures where the thermal deBroglie wavelength of the constituents is on the order of the interparticle separation. For bosonic atoms, this leads to the onset of Bose-Einstein condensation as observed for the first time in 1995 in a gas of 87 Rb at JILA [6], in 23 Na at MIT [7] and for 7 Li at Rice University [8] in the special case of attractive interactions. For fermionic atoms, the onset of degeneracy is less spectacular due to the absence of a phase transition.…”

Section: Introductionmentioning

confidence: 89%

“…On the other hand, a large class of experiments exploring degenerate gases had been studying the properties of the system in terms of atom numbers or trap frequencies, whereas in many situations the parameter which is physically interesting is the interaction, and Feshbach resonances allow this knob to be turned just by changing the magnetic field. 7 Li, for example, is a system with a strong attractive background interaction, allowing the production of BECs of only a few thousand atoms before the onset of collapse [8]. Phenomena like the collapse have first been observed by varying the atom number in the sample [82], thereby only indirectly affecting interactions through the density.…”

Section: Tuning Of Heteronuclear Interactionsmentioning

confidence: 99%

Heteronuclear quantum gas mixtures

Ospelkaus¹,

Ospelkaus²

2008

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

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Abstract. In this PhD tutorial article, we present experiments with quantum degenerate mixtures of fermionic and bosonic atoms in 3-dimensional optical lattices. This heteronuclear quantum gas mixture offers a wide range of possibilities for quantum simulation, implementation of condensed matter Hamiltonians, quantum chemistry and ultimately dense and quantum degenerate dipolar molecular samples.We When loaded into a 3D optical lattice, a whole zoo of novel quantum phases has been predicted for Fermi-Bose mixtures. We present the first realization of Fermi-Bose mixtures in 3D optical lattices as a novel quantum many body system [3]. We study the phase coherence of the bosonic cloud in the 3D optical lattice as a function of the amount of fermionic atoms simultaneously trapped in the lattice. We observe a loss of phase coherence at much lower lattice depth than for a pure bosonic cloud and discuss possible theoretical scenarios including adiabatic processes, mean field FermiBose Hubbard scenarios, and disorder-enhanced localization scenarios.After considering this many-body limit of mixtures in lattices, we show how fermionic heteronuclear Feshbach molecules can be created in the optical lattice [4] as a crucial step towards all ground state dense dipolar molecular samples. We develop rf association as a novel molecule association technique, measure the binding energy, lifetime, and association efficiency of the molecules. We develop a simple theoretical single channel model of the molecules trapped in the lattice [5] which gives excellent quantitative agreement with the experimental data.

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Bose-Einstein Condensation in a Gas of Sodium Atoms

Cited by 453 publications

References 2 publications

Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential

Rigorous derivation of the Gross-Pitaevskii equation with a large interaction potential

Breaking the superfluid speed limit in a fermionic condensate

Heteronuclear quantum gas mixtures

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