Expansion of a Coherent Array of Bose-Einstein Condensates

Pedri, P.; Pitaevskiĭ, Lev P.; Stringari, S.; Fort, C.; Burger, Sven; Cataliotti, F. S.; Maddaloni, P.; Minardi, F.; Inguscio, M.

doi:10.1103/physrevlett.87.220401

Cited by 185 publications

(233 citation statements)

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“…In particular we measure the frequencies of the quadrupole and transverse breathing modes as a function of the optical lattice depth. The experimental observations are compared with the predictions of the model reported in [16] consisting in a frequency shift of the collective modes characterized by a motion along the lattice axis, whereas the frequency of collective modes involving an atomic flow transverse respect to the periodic potential, is expected to remain unchanged.The experiment is performed with a F = 1, m F = −1 87 Rb condensate produced in the combined potential obtained superimposing a 1D optical lattice along the axial direction of a Ioffe-Pritchard magnetic trap [11,19]. The harmonic magnetic trap is characterized by a cylindrical symmetry with axial and radial frequencies respectively ν z = 8.70±0.02 Hz and ν ⊥ = 85.7±0.6 Hz.…”

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“…The experiment is performed with a F = 1, m F = −1 87 Rb condensate produced in the combined potential obtained superimposing a 1D optical lattice along the axial direction of a Ioffe-Pritchard magnetic trap [11,19]. The harmonic magnetic trap is characterized by a cylindrical symmetry with axial and radial frequencies respectively ν z = 8.70±0.02 Hz and ν ⊥ = 85.7±0.6 Hz.…”

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Collective Excitations of a Trapped Bose-Einstein Condensate in the Presence of a 1D Optical Lattice

et al. 2003

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We study low-lying collective modes of a horizontally elongated 87 Rb condensate produced in a 3D magnetic harmonic trap with the addition of a 1D periodic potential which is provided by a laser standing-wave along the horizontal axis. While the transverse breathing mode results unperturbed, quadrupole and dipole oscillations along the optical lattice are strongly modified. The measurement of frequencies of collective modes was immediately recognized to be a fundamental and precise tool to investigate the quantum macroscopic behaviour of atomic Bose-Einstein condensates. The observations of low-lying excitations [1,2,3], including the scissor mode [4], were an important step toward the characterization of these systems. Collective excitations were also studied at finite temperature [5,6,7,8] investigating frequency shifts and damping rates. All the experiments so far reported were performed on Bose-Einstein condensates magnetically trapped in pure harmonic potentials.More recently, condensates trapped in periodic potentials have attracted much interest demonstrated by the flourishing of both theoretical and experimental papers in this field. BEC trapped in a periodic potential is particularly interesting as a possible system for the investigation of pure quantum effects. Many results have been reported e.g. interference of atomic de Broglie waves tunneling from a vertical array of BECs [9], observation of squeezed states in a BEC [10], realization of a linear array of Josephson junctions [11] with BECs, observation of Bloch oscillations [12] and culminating with the observation of the quantum phase transition from a superfluid to a Mott insulator [13]. Recently, the general interest of this field has been extended to a careful study of the loading of BECs in an optical lattice [14] and to the observation of collapse and revival of the matter wave field of a BEC [15]. In this context, the characterization of collective modes of a condensate in the presence of an optical lattice motivated the development of a new theoretical treatment [16] based on a generalization of the hydrodynamic equation of superfluids for a weakly interacting Bose gas [17,18] to include the effects of the periodic potential. The collective modes of a trapped BEC are predicted to be significantly modified by the presence of an optical lattice. Precise measurements of the low-lying collective frequency would verify the validity of the mass renormalization theory [16].In this Letter we quantitatively investigate the modification of the low-lying excitation spectrum of a harmonically trapped BEC, due to the presence of a 1D optical lattice. In particular we measure the frequencies of the quadrupole and transverse breathing modes as a function of the optical lattice depth. The experimental observations are compared with the predictions of the model reported in [16] consisting in a frequency shift of the collective modes characterized by a motion along the lattice axis, whereas the frequency of collective modes involving an atomic flow transverse...

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Collective Excitations of a Trapped Bose-Einstein Condensate in the Presence of a 1D Optical Lattice

et al. 2003

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“…The ensuing dynamics is revealed by turning off, after different evolution times, both the magnetic and optical traps and imaging the atomic density distribution after an expansion time t ex p = 27.8 ms. During the expansion the different condensates, originally located at the nodes of the laser standing wave, overlap and interfere allowing us to monitor their relative phases [13].…”

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Superfluid current disruption in a chain of weakly coupled Bose–Einstein condensates

Cataliotti

Fallani²,

Ferlaino³

et al. 2003

New J. Phys.

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Abstract. We report the experimental observation of the disruption of the superfluid atomic current flowing through an array of weakly linked BoseEinstein condensates. The condensates are trapped in an optical lattice superimposed on a harmonic magnetic potential. The dynamical response of the system to a change of the magnetic potential minimum along the optical lattice axis goes from a coherent oscillation (superfluid regime) to a localization of the condensates in the harmonic trap ('classical' insulator regime). The localization occurs when the initial displacement is larger than a critical value or, equivalently, when the velocity of the wavepacket's centre of mass is larger than a critical velocity dependent on the rate of tunnelling between adjacent sites. Atomic Bose-Einstein condensates have been either loaded or produced in periodic potentials opening up the possibility of investigating new phenomena tuning the degree of coherence in the system. Experiments have explored regimes ranging from the coherent matter wave emission from a condensate loaded on a vertical standing wave [1], to the observation of number squeezed states [2], the demonstration of a one-dimensional Josephson junction array with a linear chain of condensates produced in an optical lattice [3], and the recent observation of a quantum phase transition in a condensate loaded in a 3D optical lattice [4]. The dynamical behaviour of coherent matter waves in periodic potentials has also been the subject of extensive 4

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“…Comparing the fitted frequency to Ω yields a reduction by 0.70(1), consistent with the calculated γ 0 . We note that the oscillation amplitude is slighty reduced below unity, corresponding to a finite detuning of 1.5(1) kHz in the Rabi model, which is within the systematic lattice calibration error (and comparable to differential mean-field shifts from the density compression in the lattice [27]). …”

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Nonadiabatic diffraction of matter waves

et al. 2015

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Diffraction phenomena usually can be formulated in terms of a potential that induces the redistribution of a wave's momentum. Using an atomic Bose-Einstein condensate coupled to the orbitals of a state-selective optical lattice, we investigate a hitherto unexplored nonadiabatic regime of diffraction in which no diffracting potential can be defined, and in which the adiabatic dressed states are strongly mixed. We show how, in the adiabatic limit, the observed coupling between internal and external dynamics gives way to standard Kapitza-Dirac diffraction of atomic matter waves. We demonstrate the utility of our scheme for atom interferometry and discuss prospects for studies of dissipative superfluid phenomena.Diffraction, the bending of waves around obstacles, is one of the most fundamental and ubiquitous phenomena in optics, with a centuries-old history going back to the works of Grimaldi, Huygens, and Young on the wave nature of light. In the modern era it has led to the understanding of x-rays [1, 2], has provided direct proof for the wave nature of particles [3], and today finds many applications in physics and materials science, ranging from electron, x-ray and neutron diffraction, to applications in atom optics [4,5].Quite generally, diffraction is caused by a positiondependent potential with absorptive (imaginary) and/or dispersive (real) character. While the former includes material structures and diffraction gratings, an example for the latter is the ponderomotive potential exerted on electrons by an optical standing wave, as originally suggested by Kapitza and Dirac [6]. Kapitza-Dirac diffraction of electrons was first demonstrated only fairly recently [7], well after the first observation of an analogous effect on neutral atoms based on the ac Stark shift near an atomic resonance [8]. It has also been applied to Bose-Einstein condensates [9,10] and has become an important and often-used tool in atom interferometry and metrology [5].In this paper, we investigate a hitherto unexplored regime of diffraction, in which a diffracting potential cannot be defined. In our experiment we diffract an atomic matter wave from a microwave-dressed optical lattice, with a diffractive dynamics that is qualitatively different from Kapitza-Dirac diffraction of dressed matter waves from a periodic optical potential. We note that the coherent mixing of states interacting with an external field is often used for the engineering of dressed potentials [11][12][13][14][15][16][17][18][19]. Deviations from adiabaticity have previously been found to have deleterious effects on dressed-state lifetimes [20,21]. In our experiment, we enter the strongly nonadiabatic regime, in which coherent Landau-Zener transitions of the atomic wavefunction between the adiabatic dressed potentials (driven by zero-point motion) induce a strong coupling between internal and external degrees of freedom, leading to a breakdown of the usual BornOppenheimer (adiabatic) approximation [22]. Our experimental procedure, cf. Fig. 1a, uses microwave radiation ...

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Expansion of a Coherent Array of Bose-Einstein Condensates

Cited by 185 publications

References 15 publications

Collective Excitations of a Trapped Bose-Einstein Condensate in the Presence of a 1D Optical Lattice

Collective Excitations of a Trapped Bose-Einstein Condensate in the Presence of a 1D Optical Lattice

Superfluid current disruption in a chain of weakly coupled Bose–Einstein condensates

Nonadiabatic diffraction of matter waves

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