Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor
14 Jul 1995-Science (American Association for the Advancement of Science)-Vol. 269, Iss: 5221, pp 198-201
TL;DR: A Bose-Einstein condensate was produced in a vapor of rubidium-87 atoms that was confined by magnetic fields and evaporatively cooled and exhibited a nonthermal, anisotropic velocity distribution expected of the minimum-energy quantum state of the magnetic trap in contrast to the isotropic, thermal velocity distribution observed in the broad uncondensed fraction.
Abstract: A Bose-Einstein condensate was produced in a vapor of rubidium-87 atoms that was confined by magnetic fields and evaporatively cooled. The condensate fraction first appeared near a temperature of 170 nanokelvin and a number density of 2.5 x 10 12 per cubic centimeter and could be preserved for more than 15 seconds. Three primary signatures of Bose-Einstein condensation were seen. (i) On top of a broad thermal velocity distribution, a narrow peak appeared that was centered at zero velocity. (ii) The fraction of the atoms that were in this low-velocity peak increased abruptly as the sample temperature was lowered. (iii) The peak exhibited a nonthermal, anisotropic velocity distribution expected of the minimum-energy quantum state of the magnetic trap in contrast to the isotropic, thermal velocity distribution observed in the broad uncondensed fraction.
Citations
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TL;DR: In this paper , the authors investigated the structure of the corresponding classical phase space and calculate change in the action which corresponds to finite-rate efficiency of the sweep, and considered the case of nonzero initial action, which correspond to some finite initial molecular fraction.
Abstract: Mean-field approach has recently been used to model coupled atom-molecular Bose-Einstein condensates (BEC) and coupled Fermi-Bose condensates near Feshbach resonance. Sweeping of magnetic field across the resonance gives a new (nonlinear) version of Landau-Zener problem. We investigate the structure of the corresponding classical phase space and calculate change in the action which corresponds to finite-rate efficiency of the sweep. We consider the case of nonzero initial action, which corresponds to some finite initial molecular fraction. MSC: 82B10 Quantum equilibrium statistical mechanics (general)
TL;DR: In this article, the authors studied the nonlinear effect of nonlinear collisions between particles in ultracold atomic condensate experiments and proposed a nonlinear model for producing ultracolds.
Abstract: Due to the inevitability of nonlinear collisions between particles in ultracold atomic condensate experiments, it is of great significance to study the nonlinear effect for producing ultracold mole...
TL;DR: In this article, the authors applied a many mode Floquet formalism for magnetically trapped atoms interacting with a polychromatic rf-field to predict a large two photon transition probability in the atomic system of cold 87Rb atoms.
TL;DR: In this article , the evolution of the magnetic phase diagram of S = 3/2 quantum magnet Ba 2 CoGe 2 O 7 when the averaged interaction J is controlled by a dilution of magnetic sites is studied.
Abstract: Abstract Bose–Einstein condensation (BEC) in quantum magnets, where bosonic spin excitations condense into ordered ground states, is a realization of BEC in a thermodynamic limit. Although previous magnetic BEC studies have focused on magnets with small spins of S ≤ 1, larger spin systems potentially possess richer physics because of the multiple excitations on a single site level. Here, we show the evolution of the magnetic phase diagram of S = 3/2 quantum magnet Ba 2 CoGe 2 O 7 when the averaged interaction J is controlled by a dilution of magnetic sites. By partial substitution of Co with nonmagnetic Zn, the magnetic order dome transforms into a double dome structure, which can be explained by three kinds of magnetic BECs with distinct excitations. Furthermore, we show the importance of the randomness effects induced by the quenched disorder: we discuss the relevance of geometrical percolation and Bose/Mott glass physics near the BEC quantum critical point.
TL;DR: In this article , a physically motivated model for a trapped dilute gas of Bosons with repulsive pairwise atomic interactions at zero temperature was proposed, in which the pair-excitation kernel obeys a nonlinear integro-partial differential equation.
Abstract: We study a physically motivated model for a trapped dilute gas of Bosons with repulsive pairwise atomic interactions at zero temperature. Our goal is to describe aspects of the excited many-body quantum states of this system by accounting for the scattering of atoms in pairs from the macroscopic state. We start with an approximate many-body Hamiltonian,
H
a
p
p
\mathcal {H}_{\mathrm {app}}
, in the Bosonic Fock space. This
H
a
p
p
\mathcal {H}_{\mathrm {app}}
conserves the total number of atoms. Inspired by Wu [J. Math. Phys. 2 (1961), 105–123], we apply a non-unitary transformation to
H
a
p
p
\mathcal {H}_{\mathrm {app}}
. Key in this procedure is the pair-excitation kernel, which obeys a nonlinear integro-partial differential equation. In the stationary case, we develop an existence theory for solutions to this equation by a variational principle. We connect this theory to a system of partial differential equations for one-particle excitation (“quasiparticle”-) wave functions derived by Fetter [Ann. Phys. 70 (1972), 67–101], and prove existence of solutions for this system. These wave functions solve an eigenvalue problem for a
J
J
-self-adjoint operator. From the non-Hermitian Hamiltonian, we derive a one-particle nonlocal equation for low-lying excitations, describe its solutions, and recover Fetter’s energy spectrum. We also analytically provide an explicit construction of the excited eigenstates of the reduced Hamiltonian in the
N
N
-particle sector of Fock space.
References
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Proceedings Article•
14 Jul 1996TL;DR: The striking signature of Bose condensation was the sudden appearance of a bimodal velocity distribution below the critical temperature of ~2µK.
Abstract: Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.
3,530 citations
TL;DR: The confinement and cooling of an optically dense cloud of neutral sodium atoms by radiation pressure was reported, provided by three retroreflected laser beams propagating along orthogonal axes, with a weak magnetic field used to distinguish between the beams.
Abstract: We report the confinement and cooling of an optically dense cloud of neutral sodium atoms by radiation pressure. The trapping and damping forces were provided by three retroreflected laser beams propagating along orthogonal axes, with a weak magnetic field used to distinguish between the beams. We have trapped as many as ${10}^{7}$ atoms for 2 min at densities exceeding ${10}^{11}$ atoms ${\mathrm{cm}}^{\ensuremath{-}3}$. The trap was \ensuremath{\simeq}0.4 K deep and the atoms, once trapped, were cooled to less than a millikelvin and compacted into a region less than 0.5 mm in diameter.
1,402 citations
TL;DR: In this article, the authors describe how the Phasenraum eines Lichtquants in bezug auf ein gegebenes Volumen wird in „Zellen“ von der Grose h3 aufgeteilt, i.e., the Zahl der moglichen Verteilungen der Lichtquanten einer makroskopisch definierten Strahlung unter diese Zellen liefert die Entropie.
Abstract: Der Phasenraum eines Lichtquants in bezug auf ein gegebenes Volumen wird in „Zellen“ von der Grose h3 aufgeteilt. Die Zahl der moglichen Verteilungen der Lichtquanten einer makroskopisch definierten Strahlung unter diese Zellen liefert die Entropie und damit alle thermodynamischen Eigenschaften der Strahlung.
1,329 citations
11 Jul 1988
TL;DR: This "Doppler cooling limit" results from the minimization of the detuning-dependent temperature at low laser power1.
Abstract: The generally accepted theory of laser cooling of free atoms predicts that the lowest achievable temperature is given by kaT = hγ/2, where kB is Boltzmann's constant arid γ is the natural linewidth of the transition for laser cooling. This "Doppler cooling limit" results from the minimization of the detuning-dependent temperature at low laser power1:
610 citations
"Observation of Bose-Einstein Conden..." refers background in this paper
...Of the three or four most prominent players in the development of laser cooling, two (David Wineland and Bill Phillips) are long-standing Bureau scientists; two of their most influential papers are described in this volume [6,7]....
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TL;DR: In this paper, an output coupler for Bose condensed atoms in a magnetic trap was demonstrated, where short pulses of rf radiation were used to create Bose condensates in a superposition of trapped and untrapped hyperfine states.
Abstract: We have demonstrated an output coupler for Bose condensed atoms in a magnetic trap. Short pulses of rf radiation were used to create Bose condensates in a superposition of trapped and untrapped hyperfine states. The fraction of out-coupled atoms was adjusted between 0% and 100% by varying the amplitude of the rf radiation. This configuration produces output pulses of coherent atoms and can be regarded as a pulsed ``atom laser.''
608 citations
"Observation of Bose-Einstein Conden..." refers background in this paper
...BEC is the starting point for this rapidly evolving technology— after atoms are cooled into a BEC, they are ejected out of the trap in a highly collimated, monoenergetic beam [16, 17]....
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