Gravity-induced Wannier-Stark ladder in an optical lattice

Zapata, Juan D.; Guzmán, Angela M.; Moore, M G; Meystre, Pierre

doi:10.1103/physreva.63.023607

Cited by 7 publications

(4 citation statements)

References 14 publications

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“…We will restrict our attention to the case where n 0 is of order unity. Some simple key points can be made by first considering the non-interacting case, U = 0, and also by simplifying to one spatial dimension 9 . For this special case, we can write H as…”

Section: Introductionmentioning

confidence: 99%

Mott insulators in strong electric fields

2002

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Recent experiments on ultracold atomic gases in an optical lattice potential have produced a Mott insulating state of Rb atoms. This state is stable to a small applied potential gradient (an `electric' field), but a resonant response was observed when the potential energy drop per lattice spacing (E), was close to the repulsive interaction energy (U) between two atoms in the same lattice potential well. We identify all states which are resonantly coupled to the Mott insulator for E close to U via an infinitesimal tunneling amplitude between neighboring potential wells. The strong correlation between these states is described by an effective Hamiltonian for the resonant subspace. This Hamiltonian exhibits quantum phase transitions associated with an Ising density wave order, and with the appearance of superfluidity in the directions transverse to the electric field. We suggest that the observed resonant response is related to these transitions, and propose experiments to directly detect the order parameters. The generalizations to electric fields applied in different directions, and to a variety of lattices, should allow study of numerous other correlated quantum phases.Comment: 17 pages, 14 figures; (v2) minor additions and new reference

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Section: Introductionmentioning

confidence: 99%

Mott insulators in strong electric fields

2002

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“…At the single-atom level, they were exploited extensively in theoretical and experimental work aiming at demonstrating effects such as Bloch oscillations [17][18][19], Landau-Zener tunneling [20,21], the appearance of Wannier-Stark ladders [20,[22][23][24], quantum chaos [25] and the dynamics of mesoscopic quantum superpositions [26]. The extension of this work to Bose-Einstein condensates [27,28] includes the first demonstration of a modelocked atom laser [29], a device that can also be interpreted in terms of Landau-Zener tunneling.…”

Section: Introductionmentioning

confidence: 99%

Coherent acceleration of Bose-Einstein condensates

et al. 2001

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We present a theoretical analysis of the coherent acceleration of atomic Bose-Einstein condensates. A first scheme relies on the 'conveyor belt' provided by a frequency-chirped optical lattice. For potentials shallow enough that the condensate is not fragmented, the acceleration can be interpreted in terms of sequential Bragg scattering, with the atomic sample undergoing transitions to a succession of discrete momentum sidemodes. The narrow momentum width of these sidemodes offers the possibility to accelerate an ultracold atomic sample such as e.g. a Bose-Einstein condensate without change in its momentum distribution. This is in contrast to classical point particles, for which this kind of acceleration leads to a substantial heating of the sample. A second scheme is based on the idea of a synchronous particle accelerator consisting of a spatial array of quadrupole traps. Pulsing the trapping potential creates a traveling trap that confines and accelerates the atomic system. We study this process using the concept of phase stability.

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“…Therefore the size of the cloud can have at most a variation of the order of the extension l of the single φ i . In our case, for s = 6 and F = ma, where m is the mass of the potassium atom and a = 9.8 m/s 2 , l ∼ 2µm [16]. As a consequence the spatial resolution of our interferometer depends on the initial size of the condensate if this is larger than l. Tuning a s to zero allows the condensate to occupy the ground state of the trapping potential and by an appropriate choice of the external confinement we can prepare very small samples.…”

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confidence: 84%

“…The condensate is adiabatically loaded in a sinusoidal potential with period λ/2, realized with an optical standing wave of wavelength λ. In the presence of an external force F , the macroscopic wavefunction ψ of the condensate can be described as a coherent superposition of Wannier Stark states φ i [16], parametrized with the lattice site index i, characterized by complex amplitudes of module √ ρ i and phase θ i , ψ = i √ ρ i exp(jθ i )φ i [17]. In the absence of interaction the phase of each state evolves according to the energy shift induced by the external potential, i.e.…”

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confidence: 99%

Atom Interferometry With a Weakly Interacting Bose-Einstein Condensate

Fattori¹,

Deissler²,

D’Errico³

et al. 2009

Pushing the Frontiers of Atomic Physics

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We demonstrate the operation of an atom interferometer based on a weakly interacting Bose-Einstein condensate. We strongly reduce the interaction induced decoherence that usually limits interferometers based on trapped condensates by tuning the s-wave scattering length almost to zero via a magnetic Feshbach resonance. We employ a 39 K condensate trapped in an optical lattice, where Bloch oscillations are forced by gravity. The fine-tuning of the scattering length down to 0:1 a 0 and the micrometric sizes of the atomic sample make our system a very promising candidate for measuring forces with high spatial resolution. Our technique can be in principle extended to other measurement schemes opening new possibilities in the field of trapped atom interferometry. [2,3]. Unfortunately in high density trapped condensed clouds, interaction induces phase diffusion [4] and can cause systematic frequency shifts due to uncontrolled atomic density gradient, thus seriously limiting the performances of a BEC atom interferometer. In order to avoid the deleterious effect of interaction, atom interferometers for high precision measurement use free falling dilute samples of nondegenerate atoms [5]. The main drawbacks are the limited interrogation time (0.5 s) due to the finite size of the apparatus and the poor spatial resolution of this type of sensors. Using fermionic atoms instead of bosons represents one possibility to have access to trapped interferometry with a degenerate gas [6]. In fact, because of the Pauli exclusion principle, the atomic scattering cross section at sufficiently low temperatures is fully suppressed. However, the quantum pressure limits the spatial resolution, and the momentum spread reduces the interference contrast. Another way to reduce the effect of the interaction is to realize a number squeezed splitting [7,8]. In this way, coherence times are increased at the expense of the interference signal visibility. Despite the fundamental limit represented by interaction induced decoherence, several groups are performing experiments with trapped BECs [7][8][9][10], in the challenging search for the ''ideal'' interferometer.In this Letter, we demonstrate the conceptually simplest solution to the long-standing problem of interaction induced decoherence in BEC interferometers. We show how, by properly tuning the interaction strength in a quantum degenerate gas of 39 K [11] by means of a broad magnetic Feshbach resonance [12], we can greatly increase the coherence time of an atom interferometer. By achieving almost vanishing values of the s-wave scattering length, we demonstrate trapped atom interferometry with a weakly interacting BEC.The interferometer we adopted, commonly known as Bloch oscillations interferometer, is based on a multiple well scheme [2,6,13,14]. The condensate is adiabatically loaded in a sinusoidal potential with period =2, realized with an optical standing wave of wavelength . In the presence of an external force F, the macroscopic wave function of the condensate can be described as a cohere...

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Gravity-induced Wannier-Stark ladder in an optical lattice

Cited by 7 publications

References 14 publications

Mott insulators in strong electric fields

Mott insulators in strong electric fields

Coherent acceleration of Bose-Einstein condensates

Atom Interferometry With a Weakly Interacting Bose-Einstein Condensate

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