Bloch oscillations of Bose-Einstein condensates: Breakdown and revival

Witthaut, Dirk; Werder, Mauro; Mossmann, S.; Korsch, Hans Jürgen

doi:10.1103/physreve.71.036625

Cited by 56 publications

(64 citation statements)

References 30 publications

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“…For a constant gradient ∇V , the T k obey an oscillatory time-dependence due to the periodicity in k → k + t∇V , which is the basis of the well-known Bloch oscillations [5,8]. For simplicity, we first consider the limit of small J which facilitates a perturbative solution of Eqs.…”

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confidence: 99%

Sauter-Schwinger-like tunneling in tilted Bose-Hubbard lattices in the Mott phase

2012

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We study the Mott phase of the Bose-Hubbard model on a tilted lattice. On the (Gutzwiller) mean-field level, the tilt has no effect -but quantum fluctuations entail particle-hole pair creation via tunneling. For small potential gradients (long-wavelength limit), we derive a quantitative analogy to the Sauter-Schwinger effect, i.e., electron-positron pair creation out of the vacuum by an electric field. For large tilts, we obtain resonant tunneling related to Bloch oscillations. Introduction. There are many striking analogies between apparently very different areas in physics, which help us to unify our understanding of nature -as R. Feynman said: The same equations have the same solutions. In this Letter, we establish such a quantitative analogy between high-field science and ultra-cold atoms in optical lattices. The Sauter-Schwinger effect [1][2][3] predicts that an extremely strong electric field may create electronpositron pairs out of the QED vacuum. As an intuitive picture, one can envisage this effect as tunneling of an electron from the Dirac sea into the positive continuum, leaving behind a hole (i.e., positron), see Fig. 1. Unfortunately, this prediction has not been experimentally verified yet since it is hard to generate sufficiently strong electric fields in large enough space-time regions. As we shall demonstrate below, the same equations govern particlehole pair creation in a Mott insulator via tunneling due to a small potential gradient. The Mott insulator state we are considering can be generated by bosonic atoms in an optical lattice [4,5] for example, which repel each other and thereby become effectively pinned to the lattice sites (zero mobility). The benefits of this quantitative analogy are two-fold. On the one hand, we can apply our knowledge of the Sauter-Schwinger effect [1, 2] to atoms in optical lattices and understand them better in this way. On the other hand, atoms in optical lattices may provide (via this analogy) an experimental approach to the so far unobserved Sauter-Schwinger effect.

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Sauter-Schwinger-like tunneling in tilted Bose-Hubbard lattices in the Mott phase

2012

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“…A weaker but not negligible attractive contribution comes from dis- tant sites due to the long range character of the MDI. The non-uniform population over the OL leads to a non homogeneous positive mean field shift causing dephasing of the Bloch oscillations [5,13]. A proper negative value of a reduces and flattens the interaction mean field shift, increasing the coherence time of the interferometer.…”

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Magnetic Dipolar Interaction in a Bose-Einstein Condensate Atomic Interferometer

et al. 2008

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We study the role played by the magnetic dipole interaction in an atomic interferometer based on an alkali Bose-Einstein condensate with tunable scattering length. We tune the s-wave interaction to zero using a magnetic Feshbach resonance and measure the decoherence of the interferometer induced by the weak residual interaction between the magnetic dipoles of the atoms. We prove that with a proper choice of the scattering length it is possible to compensate for the dipolar interaction and extend the coherence time of the interferometer. We put in evidence the anisotropic character of the dipolar interaction by working with two different experimental configurations for which the minima of decoherence are achieved for a positive and a negative value of the scattering length, respectively. Our results are supported by a theoretical model we develop. This model indicates that the magnetic dipole interaction should not represent a serious source of decoherence in atom interferometers based on Bose-Einstein condensates. Atom-atom interactions represent a fundamental limit to the performance of atomic Bose Einstein condensate (BEC) interferometers [1,2,3,4]. Atomic collisions lead to density-dependent shifts in the interferometric signal, severely compromising its visibility. In two recent works [5,6], the possibility to strongly reduce the interactioninduced decoherence in a trapped BEC interferometer has been demonstrated by tuning the s-wave scattering length a almost to zero via a magnetic Feshbach resonance. The tunability of a by magnetic means is possible for atoms with a non-vanishing magnetic dipole moment. Therefore, once the s-wave contact interaction is canceled by applying a proper external magnetic field, the magnetic dipole-dipole interaction (MDI) between the atoms remains as a possible source of decoherence for the interferometer. This aspect has been pointed out in [5,6], but both a theoretical analysis and an experimental study of the problem are still missing. The MDI generally does not play a role in experiments with ultra-cold quantum degenerate alkali atoms, where the small magnetic dipole moment µ is on the order of the Bohr magneton µ B and leads to a dipolar interaction energy E d < 0.01 · E s , with E s the s-wave contact interaction energy. So far, studies of the MDI in an ultra-cold gas have been possible mainly with Cr atoms [7], characterized by a large magnetic dipole moment µ = 6µ B that leads to interaction energies E d 36 times larger than for alkali atoms. Evidence of MDI in a spinorial alkali BEC has been only recently reported in [8].In this Letter we study the role played by the MDI in an interferometer where a BEC with weak tunable contact interaction is implemented [5]. We get evidence of the effect of dipolar interaction on the dephasing of the interferometric signal. The MDI is anisotropic and therefore the sign of its contribution to the interaction energy depends on the geometry of the system. We study in particular two different geometries for which the minimum of decoheren...

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“…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 coherent superposition of Wannier Stark states i [15], parametrized with the lattice site index i, characterized by complex amplitudes of module i p and phase i , P i i p exp j i i [16]. In the absence of interaction, the phase of each state evolves according to the energy shift induced by the external potential, i.e., i F it=2@.…”

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Atom Interferometry with a Weakly Interacting Bose-Einstein Condensate

et al. 2008

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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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Bloch oscillations of Bose-Einstein condensates: Breakdown and revival

Cited by 56 publications

References 30 publications

Sauter-Schwinger-like tunneling in tilted Bose-Hubbard lattices in the Mott phase

Sauter-Schwinger-like tunneling in tilted Bose-Hubbard lattices in the Mott phase

Magnetic Dipolar Interaction in a Bose-Einstein Condensate Atomic Interferometer

Atom Interferometry with a Weakly Interacting Bose-Einstein Condensate

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