Experimental realization of a momentum-space quantum walk

Abstract

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.

Resonant Quantum Kicked Rotor as A Continuous-Time Quantum Walk

“…Only recently, the experimental realization, dubbed the atom-optics kicked rotor based on (ultra)cold atoms, has been proposed as an implementation of discrete-time [16] and continuous-time [17] quantum walks in momentum space. The experimental implementation of such momentum quantum walks was largely discussed in [18,19]. Similar observations on the interference patterns in the resonant quantum kicked rotor and possible analogies with quantum walks were reported in, e.g., [20][21][22][23][24][25][26][27].…”

“…Therefore, the simple QKR at principal resonance conditions directly implements a CTQW as defined in [8]. Previously, this identity was not highlighted explicitly or was only thought to be true approximately; see the discussions in [17] and around Figure 2 in [19].…”

“…One can restore exact equivalence, for instance, by adding a phase of π to the prefactor C 0 or by implementing kicks with a negative strength κ = −2γ. This can be experimentally implemented in setups with cold atoms as in [18,19], for instance. Indeed, in that case, κ is proportional to the squared Rabi frequency and to the duration of the kick pulse, which are positive, but inversely proportional to the detuning from the atomic transition, which can have also a negative value; please see the proposal of [16] for details.…”

“…These results are then used for discussing how to engineer interesting states by means of the QKR/CTQW evolution. This is done by optimizing the starting state, which is typically limited to superpositions of just a few momentum eigenstates in the atom-optics implementation of the QKR [2][3][4][5][6][7]18,19,28].…”

Enhancing survival resonances with engineered dissipation

“…For example, dynamically varying τ 1 and pulse period T might allow the atoms to stay longer in a long-surviving mode and thereby lead to a higher survival peak. Additionally, the ability for generating periodic atomic density distributions may find applications as state preparation for quantum ratchet [34], and quantum random walk experiments [35][36][37], since it can replace the need for a Bose-Einstein condensate.…”