Phase space tomography of classical and nonclassical vibrational states of atoms in an optical lattice

Kanem, J. F.; Maneshi, Samansa; Myrskog, Stefan; Steinberg, Aephraim M.

doi:10.1088/1464-4266/7/12/037

Cited by 12 publications

(6 citation statements)

References 31 publications

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“…Figure 3 shows the results of quantum simulations graphing energy absorption in recoil energies after 16 kicks versus kick period (and˜ /π) for k = 1.6. There is a strong sharp resonance at˜ = 2π as well as a higher order one at˜ = π, and less well resolved high-order resonances at˜ ∼ deep lattice, a state we can readily prepare [19]. This gives a spatial width of x 0 = 0.109 µm which localizes each wavepacket entirely within one well.…”

Section: Where θ T Is the Heaviside Step Function Equation (3) Then mentioning

confidence: 99%

Observation of High-Order Quantum Resonances in the Kicked Rotor

et al. 2007

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Quantum resonances in the kicked rotor are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances occur when the scaled Planck's constant˜ = r s · 4π, for any integers r and s. However only the˜ = r · 2π resonances are easily observable. We have observed high-order quantum resonances (s > 2) utilizing a sample of low temperature, non-condensed atoms and a pulsed optical standing wave. Resonances are observed for˜ = r 16 · 4π for integers r = 2 − 6. Quantum numerical simulations suggest that our observation of high-order resonances indicates a larger coherence length than expected from an initially thermal atomic sample.PACS numbers: 05.45. Mt, 32.80.Pj, 32.80.Lg A rotor subjected to a periodically pulsed sinusoidal potential ("kicked rotor") is one of the most widely studied paradigms of chaotic dynamics. Ever since the qualitative differences between the classical kicked rotor and the quantum kicked rotor (QKR) became evident [1], the QKR has proven to be a rich system for studying quantum-classical correspondence, decoherence, and quantum dynamics in general. To this day the study of the standard QKR as well as alternative kicked rotor Hamiltonians [2,3] is an actively pursued field. Much of the early work was done through theoretical and numerical analysis, with one of the more important discoveries being the realization that momentum localization in the QKR can be thought of as a form of Anderson localization [4]. An experimental breakthrough in the field came when laser cooling and optical trapping of atoms allowed the use of optical lattices as a linear momentum analogue of the QKR. This led to the observation of some of the theoretical predictions such as momentum localization [5] as well as studies of decoherence [6] and interesting results arising from modifications to the Hamiltonian of the QKR [7,8].Quantum resonances [5,9] are another aspect of the QKR which have been of experimental interest recently: for certain parameters, heating is greatly enhanced in contrast to the momentum localization usually present in the quantum kicked rotor. In the presence of gravity or other linear potentials one sees accelerator modes[10], similar to quantum resonances except that there is an increase in average momentum as well as momentum spread. Like other aspects of the quantum kicked rotor, quantum resonances are useful for studying quantumclassical correspondence. Work has gone into studying the effect in the presence of noise and the competition with momentum localization and the resonances [11].Here we present experimental observation of quantum resonances utilizing a sample of cold thermal rubidium atoms in an optical lattice. Specifically, we report our observation of high-order quantum resonances. There have been studies of high-order accelerator modes previously [12] as well as a concurrent observation of highorder resonances in a Bose-Einstein condensate [13]. In all previous experiments with nondegenerate at...

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Section: Where θ T Is the Heaviside Step Function Equation (3) Then mentioning

confidence: 99%

Observation of High-Order Quantum Resonances in the Kicked Rotor

et al. 2007

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“…We consider a physical model of the optical lattice similar to the experimental apparatus described in Refs [11,31,32]. The optical lattice potential is generated by two vertical counter-propagating lasers with an incidence angle of 49.6 • and is loaded with 85 Rb atoms from an optical molasses at 10 µK.…”

Section: A Modelmentioning

confidence: 99%

High-fidelity quantum gates in the presence of dispersion

et al. 2012

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We numerically demonstrate the control of motional degrees of freedom of an ensemble of neutral atoms in an optical lattice with a shallow trapping potential. Taking into account the range of quasimomenta across different Brillouin zones results in an ensemble whose members effectively have inhomogeneous control fields as well as spectrally distinct control Hamiltonians. We present an ensemble-averaged optimal control technique that yields high fidelity control pulses, irrespective of quasimomentum, with average fidelities above 98%. The resulting controls show a broadband spectrum with gate times in the order of several free oscillations to optimize gates with up to 13.2% dispersion in the energies from the band structure. This can be seen as a model system for the prospects of robust quantum control. This result explores the limits of discretizing a continuous ensemble for control theory.

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“…The optical homodyne tomography reconstructs the quantum state of light by directly measuring the planar Radon transform of the Wigner function [43,44]. Also, the Husimi Q function [45] has been experimentally measured for various systems [23,32,34,36,[46][47][48]. We detail how to tomographically reconstruct a class of finite-dimensional phase-space representations.…”

Section: Introductionmentioning

confidence: 99%

Continuous phase-space representations for finite-dimensional quantum states and their tomography

2020

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Continuous phase spaces have become a powerful tool for describing, analyzing, and tomographically reconstructing quantum states in quantum optics and beyond. A plethora of these phasespace techniques are known, however a thorough understanding of their relations was still lacking for finite-dimensional quantum states. We present a unified approach to continuous phase-space representations which highlights their relations and tomography. The infinite-dimensional case from quantum optics is then recovered in the large-spin limit. * balint.koczor@materials.ox.ac.uk

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Phase space tomography of classical and nonclassical vibrational states of atoms in an optical lattice

Cited by 12 publications

References 31 publications

Observation of High-Order Quantum Resonances in the Kicked Rotor

Observation of High-Order Quantum Resonances in the Kicked Rotor

High-fidelity quantum gates in the presence of dispersion

Continuous phase-space representations for finite-dimensional quantum states and their tomography

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