Steering random walks with kicked ultracold atoms

Weiß, Marcel; Groiseau, Caspar; Lam, W. K.; Burioni, Raffaella; Vezzani, A.; Summy, Gil; Wimberger, Sandro

doi:10.1103/physreva.92.033606

Cited by 21 publications

(24 citation statements)

References 50 publications

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“…with J's being Bessel functions of the first kind, represents the "kick" by each pulse that leads to a symmetric diffraction of the wave function in the space spanned by the momentum eigenstates [48]. The prefactor e −ik , which originates from the dc component of the lattice potential, introduces a "global" phase to the atoms at each kick [49,50].…”

Section: Discrete-time Quantum Walks In Momentum Spacementioning

confidence: 99%

“…While the AOKR itself can also produce ballistic expansion, the quantum resonant motion in its case would be symmetric and equal for both internal states [45,48,52]. We implement one of the requirements of a discrete-time QW by a quantum resonance ratchet effect [40][41][42], such that the two internal states move in opposite directions during the kick evolution.…”

Section: Discrete-time Quantum Walks In Momentum Spacementioning

confidence: 99%

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Experimental realization of a momentum-space quantum walk

et al. 2019

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We report on a discrete-time quantum walk that uses the momentum of ultra-cold rubidium-87 atoms as the walk space and two internal atomic states as the coin degree of freedom. Each step of the walk consists of a coin toss (a microwave pulse) followed by a unitary shift operator (a resonant ratchet pulse). We carry out a comprehensive experimental study on the effects of various parameters, including the strength of the shift operation, coin parameters, noise, and initialization of the system on the behavior of the walk. The walk dynamics can be well controlled in our experiment; potential applications include atom interferometry and engineering asymmetric walks.

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Section: Discrete-time Quantum Walks In Momentum Spacementioning

confidence: 99%

Section: Discrete-time Quantum Walks In Momentum Spacementioning

confidence: 99%

Experimental realization of a momentum-space quantum walk

et al. 2019

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“…We now make use of the wavefunctions obtained via the methods outlined above to study the population dynamics and field-free evolution of a polar and polarizable rotor subject to unipolar pulses/kicks. We restrict our discussion to a specific range of kick strengths, 10]. This implies that the wavepacket typically comprises a moderate number of rotational states -about 30 for ultra-short pulses and fewer for longer pulses.…”

Section: Resultsmentioning

confidence: 99%

“…In particular, the study of the effects on atoms and molecules of ultra-short ( picosecond) laser pulses and the kicks, whether single or multiple, they exert has matured into a broad field of research with a plethora of applications in science and technology, cf., e.g., Refs. [10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime

Mirahmadi

Schmidt

Karra

et al. 2018

The Journal of Chemical Physics

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We study, analytically as well as numerically, the dynamics that arises from the interaction of a polar polarizable rigid rotor with single unipolar electromagnetic pulses of varying length, ∆τ , with respect to the rotational period of the rotor, τ r . In the sudden, non-adiabatic limit, ∆τ τ r , we derive analytic expressions for the rotor's wavefunctions, kinetic energies, and field-free evolution of orientation and alignment. We verify the analytic results by solving the corresponding timedependent Schrödinger equation numerically and extend the temporal range of the interactions considered all the way to the adiabatic limit, ∆τ τ r , where general analytic solutions beyond the field-free case are no longer available. The effects of the orienting and aligning interactions as well as of their combination on the post-pulse populations of the rotational states are visualized as functions of the orienting and aligning kick strengths in terms of populations quilts. Quantum carpets that encapsulate the evolution of the rotational wavepackets provide the space-time portraits of the resulting dynamics. The population quilts and quantum carpets reveal that purely orienting, purely aligning, or even-break combined interactions each exhibit a sui generis dynamics. In the intermediate temporal regime, we find that the wavepackets as functions of the orienting and aligning kick strengths show resonances that correspond to diminished kinetic energies at particular values of the pulse duration. * burkhard.schmidt@fu-berlin.de † bretislav.friedrich@fhi-berlin.mpg.de arXiv:1806.11329v3 [quant-ph] 9 Aug 2018 basis set for expanding the time-dependent wavefunction, with the resultwhere E J = J(J + 1). Note that the expansion coefficients, C J J 0 ,M 0 , are time-independent, in consequence of the fact that the time dependence in Eq. (10) only arises from the e −iJ 2 τ term.The final form of the wavefunction in the sudden limit is given by (for a detailed derivationare the Clebsch-Gordan coefficients and only c J is a function of the kick strengths, cf. Eq. (A5).Throughout the remainder of this paper, we restrict ourselves to the case when the free rotor is initially in its ground state, J 0 = M 0 = 0. As a result, the C J J 0 ,M 0 coefficients in Eq. (11) reduce toThe coefficients C J J 0 ,M 0 arising in Eq. (11) can be found by expanding the time-independent term in Eq. (10) in terms of spherical harmonics,with Γ the gamma function; we applied the Legendre duplication formula [49] to achieve the final form of Eq. (A4).By making use of Eq. (A2) and Eq. (A5) we can evaluateC J J 0 ,M 0 in Eq. (A1) as follows,where J 1 M 1 , J 2 M 2 |J 3 M 3 are the Clebsch-Gordan coefficients, which vanish unless |J −J 0 | ≤ J ≤ J + J 0 and J + J + J 0 is an even integer [49]. Finally, we obtainIn all the analytic results presented in this paper, Eqs. (A5) and (A7) were found to converge satisfactorily for κ and J up to 80 and 50, respectively (e.g. for P η = P ζ = 8 the 80th term of the sum over k in Eq. (A5) is close to 10 −30 for C 50 0,0 ≈ 1...

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“…Simultaneously, the kick potential was shifted by a phase φ j randomly drawn from a uniform distribution within the interval ∆ φ × [−π; π]. A similar procedure was used in [45] to model the AOKR dynamics without the extra internal degree of freedom.…”

Section: Numerical Simulations: Quantum-to-classical Transitionsmentioning

confidence: 99%

Impact of Lattice Vibrations on the Dynamics of a Spinor Atom-Optics Kicked Rotor

et al. 2019

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We investigate the effect of amplitude and phase noise on the dynamics of a discrete-time quantum walk and its related evolution. Our findings underline the robustness of the motion with respect to these noise sources, and can explain the stability of quantum walks that has recently been observed experimentally. This opens the road to measure topological properties of an atom-optics double kicked rotor with an additional internal spin degree of freedom.

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Steering random walks with kicked ultracold atoms

Cited by 21 publications

References 50 publications

Experimental realization of a momentum-space quantum walk

Experimental realization of a momentum-space quantum walk

Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime

Impact of Lattice Vibrations on the Dynamics of a Spinor Atom-Optics Kicked Rotor

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