Atomic motion in tilted optical lattices: an analytical approach

Thommen, Quentin; Garreau, Jean Claude; Zehnlé, Véronique

doi:10.1088/1464-4266/6/7/007

Cited by 21 publications

(34 citation statements)

References 30 publications

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“…This is demonstrated by observing in situ the breathing of the wavefunction under non-resonant driving conditions, and through a self-interference technique based on time-of-flight (TOF) expansion. Our experimental findings are supported by a theoretical model with which we can determine analytically the spatial wavefunction under the action of the driving 18,19 . To drive (that is, modulate) the phase of the lattice potential, we apply a sinusoidal voltage (with frequency ν PZT ) to the piezoelectric transducer (PZT) that supports the retro-reflecting mirror of the standing-wave dipole trap (Fig.…”

supporting

confidence: 72%

“…With ν equal to +5 and −5 Hz, the breathing shows a revival with the expected period of 5 Hz, and a constant visibility on a 1 s timescale, regardless of the sign of the frequency detuning. With ν = 0.5 Hz, again the atomic distribution shows a breathing at a frequency equal to ν, and from the reduction of the oscillation amplitude over time we can infer a e −1 damping time of 28 s. The results presented in Figs 1 and 2 cannot be explained classically and show a quantitative agreement with the analytic expression of the wavefunction expected for the driven potential 18,19 . This implies that we manipulate and directly observe the spatial wavefunction on a length scale larger than 1 mm.…”

supporting

confidence: 72%

“…The spatial profile is initially Gaussian, corresponding to the initial spatial distribution of the atoms in the magneto-optical trap. The profile then evolves into a more complex shape as a result of the wavefunction broadening 18,19 , but then at the revival the distribution returns to its initial profile. Starting from a size of 31 µm, it reaches an extension larger than 1.5 mm, and then it returns to a size of 40 µm.…”

mentioning

confidence: 99%

“…The dynamics that we observe, both in situ and in TOF, can be described starting from the expression of the broadened wavefunction 18,19 …”

mentioning

confidence: 99%

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Engineering the quantum transport of atomic wavefunctions over macroscopic distances

et al. 2009

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The manipulation of matter waves had an important role in the history of quantum mechanics. The first experimental validation of matter-wave behaviour was the observation of diffraction of matter by crystals 1 , followed by interference experiments with electrons, neutrons, atoms and molecules using gratings and Young's double slit [2][3][4][5] . More recently, matter-wave manipulation has become a building block for quantum devices such as quantum sensors 6 and it has an essential role in a number of proposals for implementing quantum computers 7,8 . Here, we demonstrate the coherent control of the spatial extent of an atomic wavefunction by reversibly stretching and shrinking the wavefunction over a distance of more than one millimetre. The quantum-coherent process is fully deterministic, reversible and in quantitative agreement with an analytical model. The simplicity of its experimental implementation could ease applications in the field of quantum transport and quantum processing.Cold atomic gases trapped in optical lattices (large and periodic ensembles of optical microtraps created by interfering optical laser beams) provide ideal tools for studying quantum transport in different regimes 9,10 and quantum many-body systems in periodic potentials [11][12][13][14][15] . One of the challenges in this field is to coherently transfer matter waves between macroscopically separated sites. This would provide a mechanism to couple distant quantum bits and ultimately would lead to scalable quantum-information processing with cold atoms in optical lattices 16 . Recently, it was demonstrated that spatially driven lattice potentials in the presence of a linear potential can induce a coherent delocalization of a matter wave 17 when the driving is applied at the Bloch frequency ν B , that is, the linear potential between adjacent sites expressed in frequency units. The delocalization occurs at integer multiples of ν B because of the resonant coupling between Wannier-Stark levels within the same band. The resonances are characterized by a sinc 2 (π t ν) spectral profile, where t is the driving time and ν is the detuning of the driving from the resonant frequency. The sinc response here arises from the influence on the tunnelling current of the relative phase φ between the driving and the site-to-site quantum phase in the broadened wavefunction. When φ lies between 0 and π the wavefunction expands, whereas when it lies between π and 2π the wavefunction shrinks. In particular, when φ = 2π the wavefunction returns to the starting point. Such a reversible behaviour is expected provided that the evolution of the wavefunction is fully coherent.Any mechanism introducing loss of coherence would in fact lead to a non-reversible broadening. However, in a decoherence-free regime, it should be possible to engineer the spatial extension of the wavefunction using the frequency offset and the amplitude of the driving as tuning knobs. Here, we experimentally demonstrate this new technique of matter-wave manipulation by showing that coher...

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supporting

confidence: 72%

supporting

confidence: 72%

mentioning

confidence: 99%

“…The dynamics that we observe, both in situ and in TOF, can be described starting from the expression of the broadened wavefunction 18,19 …”

mentioning

confidence: 99%

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Engineering the quantum transport of atomic wavefunctions over macroscopic distances

et al. 2009

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“…An alternative tight-binding approach using an expansion in the eigenstates of the Wannier-Stark Hamiltonian (1) for a constant field can be found in [12].…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional Bloch oscillations: a Lie-algebraic approach

Mossmann¹,

Schulze²,

Witthaut³

et al. 2005

J. Phys. A: Math. Gen.

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A Lie-algebraic approach successfully used to describe one-dimensional Bloch oscillations in a tight-binding approximation is extended to two dimensions. This extension has the same algebraic structure as the one-dimensional case while the dynamics shows a much richer behaviour. The Bloch oscillations are discussed using analytical expressions for expectation values and widths of the operators of the algebra. It is shown under which conditions the oscillations survive in two dimensions and the centre of mass of a wave packet shows a Lissajous like motion. In contrast to the one-dimensional case, a wavepacket shows systematic dispersion that depends on the direction of the field and the dispersion relation of the field free system.

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Directed transport in quantum star graphs

Yusupov

Dolgushev

Blumen

et al. 2016

Quantum Inf Process

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We study the quantum dynamics of Gaussian wave packets on star graphs whose arms feature each a periodic potential and an external time-dependent field. Assuming that the potentials and the field can be manipulated separately for each arm of the star, we show that it is possible to manipulate the direction of the motion of a Gaussian wave packet through the bifurcation point by a suitable choice of the parameters of the external fields. In doing so, one can achieve a transmission of the wave packet into the desired arm with nearly 70% while also keeping the shape of the wave packet approximately intact. Since a star graph is the simplest element of many other complex graphs, the obtained results can be considered as the first step to wave packet manipulations on complex networks.

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Atomic motion in tilted optical lattices: an analytical approach

Cited by 21 publications

References 30 publications

Engineering the quantum transport of atomic wavefunctions over macroscopic distances

Engineering the quantum transport of atomic wavefunctions over macroscopic distances

Two-dimensional Bloch oscillations: a Lie-algebraic approach

Directed transport in quantum star graphs

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