Quantum to classical walk transitions tuned by spontaneous emissions

Clark, J. H.; Groiseau, Caspar; Shaw, Zachary; Dadras, Siamak; Binegar, Cosmo; Wimberger, Sandro; Summy, Gil; Liu, Y.

doi:10.1103/physrevresearch.3.043062

Cited by 8 publications

(30 citation statements)

References 21 publications

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“…This is the so-called quantum resonant regime of the kicked rotor [24][25][26]. In this regime the evolution well approximates an ideal quantum walk as suggested in [27] and subsequently realised in [19][20][21], in particular for kick strengths of the order k ≈ 1.5, for which the kicks dominantly couple nearest-neighbor momentum states. There is another important difference to ideal quantum walks: the kicked-rotor dynamics for both internal states would be completely symmetric in momentum space if the parity symmetry was not broken.…”

Section: The Experimental Setupmentioning

confidence: 67%

“…We are looking at a one-dimensional DTQW [8] in the following, as it was realised in [19][20][21] using a rubidium Bose-Einstein condensate. The Hilbert space for this system is given by H = H C ⊗ H P , where H C is the two-state coin space, spanned by the orthonormal basis {|0 C , |1 C }(corresponding to the two ground state hyperfine levels of rubidium) and H P represents the infinite walker's space spanned by {|n ; n ∈ Z} (corresponding to the center-of-mass momentum of the rubidium Bose-Einstein condensate).…”

Section: The Experimental Setupmentioning

confidence: 99%

“…with three real parameters α, γ and χ (the "Euler" angles of the spin-state rotation) and is realized with microwave radiation addressing the hyperfine levels of rubidium. In contrast to [15] we do not study an ideal quantum walk with exclusively nearest-neighbor couplings but a realisation based on the quantum kicked rotor [24][25][26] with a Bose-Einstein condensate subject to time-periodic kicks from a standing-wave laser [19][20][21].…”

Section: The Experimental Setupmentioning

confidence: 99%

“…We check whether a similar experiment could, in principle, be performed using a Bose-Einstein condensate (BEC) which is subject to kicks in momentum space. The latter realisation was successfully used so far to implement DTQWs up to about 20 steps [19][20][21]. The coin operation in this experiment is done shining microwave (MW) pulses onto the atoms of the condensate of which two internal states act as a qubit or spin-1/2 coin-state space.…”

Section: Introductionmentioning

confidence: 99%

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Parrondo’s Paradox for Discrete-Time Quantum Walks in Momentum Space

2022

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We investigate the possibility of implementing a sequence of quantum walks whose probability distributions give an overall positive winning probability, while it is negative for the single walks (Parrondo’s paradox). In particular, we have in mind an experimental realization with a Bose–Einstein condensate in which the walker’s space is momentum space. Experimental problems in the precise implementation of the coin operations for our discrete-time quantum walks are analyzed in detail. We study time-dependent phase fluctuations of the coins as well as perturbations arising from the finite momentum width of the condensate. We confirm the visibility of Parrondo’s paradox for experimentally available time scales of up to a few hundred steps of the walk.

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Section: The Experimental Setupmentioning

confidence: 67%

Section: The Experimental Setupmentioning

confidence: 99%

Section: The Experimental Setupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parrondo’s Paradox for Discrete-Time Quantum Walks in Momentum Space

2022

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“…Even if the atom would return to the initial ground-state level, it receives a recoil changing its quasimomentum (see below after Eq. ( 7)) and hence its response to the kicking pulses [18,19]. This implies that it will be effectively lost from the signal, and only potentially contributing to an incoherent background [14,20].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Classical model for survival resonances close to Talbot time

Andersen,

Wimberger

2022

Preprint

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We present a classical approximation for the peaks of survival resonances occurring when diffracting matter waves from absorption potentials. Generally our simplified model describes the absorption-diffraction process around the Talbot time very well. Classical treatments of this process are presently lacking. For purely imaginary potentials, the classical model duplicates quantum mechanical calculations. The classical model allows for simple evolution of phase-space probability densities, which in the limit of the effective Planck's constant going to zero allows for a compact analytical expression of the survival probability as a function of remaining parameters. Our work extends the range of processes that can be described through classical analogues.

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Feedback‐Assisted Quantum Search by Continuous‐Time Quantum Walks

et al. 2022

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The quantum search of a target node on a cycle graph by means of a quantum walk assisted by continuous measurement and feedback are addressed. Unlike previous spatial search approaches, where the oracle is described as a projector on the target state, a dynamical oracle implemented through a feedback Hamiltonian is considered. The idea is based on continuously monitoring the position of the quantum walker on the graph and then applying a unitary feedback operation based on the information obtained from measurement. The feedback changes the couplings between the nodes and it is optimized at each time via a numerical procedure. The stochastic trajectories describing the evolution for graphs of dimensions up to N = 15 are numerically simulated, and the performance of the protocol is quantified via the average fidelity between the state of the walker and the target node. Different constraints on the control strategy are discussed. For unbounded controls, the protocol is able to quickly localize the walker on the target node. How the performance is lowered by posing an upper bound on the control couplings is then discussed. Finally, it is shown how a digital feedback protocol seems in general as efficient as the continuous bounded one.

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Quantum to classical walk transitions tuned by spontaneous emissions

Cited by 8 publications

References 21 publications

Parrondo’s Paradox for Discrete-Time Quantum Walks in Momentum Space

Parrondo’s Paradox for Discrete-Time Quantum Walks in Momentum Space

Classical model for survival resonances close to Talbot time

Feedback‐Assisted Quantum Search by Continuous‐Time Quantum Walks

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