Phase-space tomography of matter-wave diffraction in the Talbot regime

Lee, S. K.; Kim, M. S.; Szewc, Carola

doi:10.1088/1367-2630/14/4/045001

Cited by 5 publications

(6 citation statements)

References 33 publications

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“…C xv can reveal the fingerprint of the underlying model and in particular is essential for understanding concepts and techniques such as adiabatic cooling in lattices [24], stochastic cooling [25], point source atom interferometry [26,27] and enhanced velocity resolution [28,29], alongside elementary notions in quantum mechanics [30]. These correlations have been surprisingly overlooked in both theory and experiment, perhaps due to the lack of a direct method for imaging the phasespace of atomic clouds, which does not require cumbersome mathematical tools or a specific potential [31][32][33][34][35]. No analysis of the dynamics of the correlations has been reported to the best of our knowledge.…”

mentioning

confidence: 99%

Observing Power-Law Dynamics of Position-Velocity Correlation in Anomalous Diffusion

et al. 2017

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In this letter we present a measurement of the phase-space density distribution (PSDD) of ultracold 87 Rb atoms performing 1D anomalous diffusion. The PSDD is imaged using a direct tomographic method based on Raman velocity selection. It reveals that the position-velocity correlation function Cxv(t) builds up on a timescale related to the initial conditions of the ensemble and then decays asymptotically as a power-law. We show that the decay follows a simple scaling theory involving the power-law asymptotic dynamics of position and velocity. The generality of this scaling theory is confirmed using Monte-Carlo simulations of two distinct models of anomalous diffusion.The phase-space density distribution (PSDD) contains information concerning the degrees of freedom of a system and allows calculation of any observable. An intriguing system to look at in this context is that of anomalous dynamics for which the mean square displacement (MSD) scales as x 2 ∼ t 2α , with α = 1/2. This type of dynamics, found in a wide variety of systems in nature ranging from dynamics of "bubbles" in denaturing DNA molecules [1], through fluctuations in the stockmarket [2] to models describing brief awakenings in the course of a night's sleep [3], is generally non-universal and system-dependent [4][5][6].A uniquely interesting model system for the study of anomalous diffusion is that of cold atoms diffusing in a dissipative 1D lattice, closely related to Lévy walks and motion in logarithmic potentials, displaying such phenomena as the breakdown of ergodicity and of equipartition, memory effects and slow relaxation to equilibrium [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The major advantage of such a system is the high degree of control it enables over the physical parameters governing the dynamics. One of the fundamental insights that can be obtained from the PSDD of such a system is the phase-space cross correlation between position and velocity C xv . C xv can reveal the fingerprint of the underlying model and in particular is essential for understanding concepts and techniques such as adiabatic cooling in lattices [24], stochastic cooling [25], point source atom interferometry [26,27] and enhanced velocity resolution [28,29], alongside elementary notions in quantum mechanics [30]. These correlations have been surprisingly overlooked in both theory and experiment, perhaps due to the lack of a direct method for imaging the phasespace of atomic clouds, which does not require cumbersome mathematical tools or a specific potential [31][32][33][34][35]. No analysis of the dynamics of the correlations has been reported to the best of our knowledge.In this letter we analyze and measure the dynamics of the position-velocity correlation of an ensemble of classical particles, originating from a point-like source and undergoing one-dimensional anomalous super-diffusion. The measurement is done using a new tomographic method for direct phase-space imaging, utilizing a combination of the straightforward tools of absorpt...

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confidence: 99%

Observing Power-Law Dynamics of Position-Velocity Correlation in Anomalous Diffusion

et al. 2017

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“…This is an important point as it allows for the extraction of both quadratures independently in order to reconstruct the state and is at the heart of each homodyne detection. By using all marginal distributions and applying the inverse Radon transformation [40] we obtain the Wigner function of the thermal state of motion of the particle, as shown in Fig. 2(c).…”

Section: Experimental Implementations and Resultsmentioning

confidence: 99%

“…This method, where we consider a single system and continuous measurements of the quadrature, could be combined with the quantum-state sampling method [37][38][39]: the reconstructed state is updated, increasing the accuracy of the reconstruction, by each new recorded value of the quadrature. However, in this paper, we adopt the inverse Radon transformation to reconstruct the Wigner function [40].…”

Section: Theoretical Descriptionmentioning

confidence: 99%

Wigner Function Reconstruction in Levitated Optomechanics

Rashid¹,

Toroš²

2017

Quantum Measurements and Quantum Metrology

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Abstract:We demonstrate the reconstruction of the Wigner function from marginal distributions of the motion of a single trapped particle using homodyne detection. We show that it is possible to generate quantum states of levitated optomechanical systems even under the e ect of continuous measurement by the trapping laser light. We describe the opto-mechanical coupling for the case of the particle trapped by a free-space focused laser beam, explicitly for the case without an optical cavity. We use the scheme to reconstruct the Wigner function of experimental data in perfect agreement with the expected Gaussian distribution of a thermal state of motion. This opens a route for quantum state preparation in levitated optomechanics.

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“…Furthermore, sideband spectroscopy is a vital tool to study the motion of trapped ions [51]. Building upon these previous techniques it has recently been theoretically proposed how to perform Wigner reconstruction of the motion of trapped particles [74] and large molecules in diffraction experiments [75].…”

Section: Mechanical Quadrature Measurementmentioning

confidence: 99%

Towards optomechanical quantum state reconstruction of mechanical motion

2014

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Utilizing the tools of quantum optics to prepare and manipulate quantum states of motion of a mechanical resonator is currently one of the most promising routes to explore non-classicality at a macroscopic scale. An important quantum optomechanical tool yet to be experimentally demonstrated is the ability to perform complete quantum state reconstruction. Here, after providing a brief introduction to quantum states in phase space, the current proposals for state reconstruction of mechanical motional states are reviewed and contrasted and experimental progress is discussed. Furthermore, it is shown that mechanical quadrature tomography using back-action-evading interactions gives an s-parameterized Wigner function where the numerical parameter s is directly related to the optomechanical measurement strength. The effects of classical noise in the optical probe for both state reconstruction and state preparation by measurement are also discussed.

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Phase-space tomography of matter-wave diffraction in the Talbot regime

Cited by 5 publications

References 33 publications

Observing Power-Law Dynamics of Position-Velocity Correlation in Anomalous Diffusion

Observing Power-Law Dynamics of Position-Velocity Correlation in Anomalous Diffusion

Wigner Function Reconstruction in Levitated Optomechanics

Towards optomechanical quantum state reconstruction of mechanical motion

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