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arXiv:2602.12767 · Physical Review A

Preparing Quantum Backflow States by Large Momentum Transfer

Yuchong Chen, Yijun Tang

quant-phSubmitted Feb 13, 2026• Announced Feb 16, 2026• 0 citations
v1 · Feb 13, 2026v2 · May 21, 2026
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Abstract

A quantum backflow state refers to a quantum state exhibiting negative probability density flux albeit a completely positive momentum spectrum. Extending earlier work that uses single laser pulse to prepare quantum backflow state in an ultracold atomic BEC [1], we theoretical investigated flexible quantum backflow state preparation via large momentum transfer technique, which to our knowledge, has not been studied before. By combining atom interferometry theory and non-interacting BEC wave function, we solve for the evolution of a BEC wavepacket under atom interferometry sequence. Simulation results show a highly tunable backflow flux and critical density under our scheme, and can be manipulated to go beyond existing numbers.

Journal reference
Phys. Rev. A 113, 063304 (2026)
DOI
10.1103/3b4f-6nfr

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A quantum backflow state refers to a quantum state exhibiting negative probability density flux albeit a completely positive momentum spectrum. Extending earlier work that uses single laser pulse to prepare quantum backflow state in an ultracold atomic BEC [1], we theoretical investigated flexible quantum backflow state preparation via large momentum transfer technique, which to our knowledge, has not been studied before. By combining atom interferometry theory and non-interacting BEC wave function, we solve for the evolution of a BEC wavepacket under atom interferometry sequence. Simulation results show a highly tunable backflow flux and critical density under our scheme, and can be manipulated to go beyond existing numbers.
Quantum backflow is a classically forbidden effect consisting of a negative flux for states with negligible negative-momentum components. It has never been observed experimentally so far. We derive a general relation that connects backflow with a critical value of the particle density, paving the way for the detection of backflow by a density measurement. To this end, we propose an explicit scheme with Bose-Einstein condensates, at reach with current experimental technologies. Remarkably, the application of a positive-momentum kick, via a Bragg pulse, to a condensate with a positive velocity may cause a current flow in the negative direction.
We present a Raman atom interferometer using large momentum transfer without reversing the direction of the effective wave vector ( k -reversal). More specifically, we use a microwave π / 2 pulse to manipulate the spin state of Rb 87 atoms before applying a Raman light π pulse to achieve 4 ℏ k momentum transfer per Raman light pulse. A microwave π pulse in the middle of the interferometer sequence reverses the spin states, which allows closing of the interferometer arms by the same Raman light π pulses without propagation reversal. We present a proof-of-principle demonstration of a 4 ℏ k large-momentum-transfer (LMT) atom interferometer and discuss its scalability. Our results extend the scope of using LMT atom optics.
We present a cold-atom gravimeter operating with a sample of Bose-condensed 87{}^{87}87Rb atoms. Using a Mach-Zehnder configuration with the two arms separated by a two-photon Bragg transition, we observe interference fringes with a visibility of ($83\ifmmode\pm\else\textpm\fi{}6$)% at T=3T=3T=3 ms. We exploit large momentum transfer (LMT) beam splitting to increase the enclosed space-time area of the interferometer using higher-order Bragg transitions and Bloch oscillations. We also compare fringes from condensed and thermal sources and observe a reduced visibility of ($58\ifmmode\pm\else\textpm\fi{}4$)% for the thermal source. We suspect the loss in visibility is caused partly by wave-front aberrations, to which the thermal source is more susceptible due to its larger transverse momentum spread. Finally, we discuss briefly the potential advantages of using a coherent atomic source for LMT, and we present a simple mean-field model to demonstrate that with currently available experimental parameters, interaction-induced dephasing will not limit the sensitivity of inertial measurements using freely falling, coherent atomic sources.
We report the first realization of large momentum transfer (LMT) clock atom interferometry. Using single-photon interactions on the strontium ^{1}S_{0}-^{3}P_{1} transition, we demonstrate Mach-Zehnder interferometers with state-of-the-art momentum separation of up to 141 ℏk and gradiometers of up to 81 ℏk. Moreover, we circumvent excited state decay limitations and extend the gradiometer duration to 50 times the excited state lifetime. Because of the broad velocity acceptance of the interferometry pulses, all experiments are performed with laser-cooled atoms at a temperature of 3 μK. This work has applications in high-precision inertial sensing and paves the way for LMT-enhanced clock atom interferometry on even narrower transitions, a key ingredient in proposals for gravitational wave detection and dark matter searches.
In its standard formulation, quantum backflow is a classically impossible phenomenon in which a free quantum particle in a positive-momentum state exhibits a negative probability current. Recently, Miller et al. [Quantum 5, 379 (2021)] have put forward a new, "experiment-friendly" formulation of quantum backflow that aims at extending the notion of quantum backflow to situations in which the particle's state may have both positive and negative momenta. Here, we investigate how the experiment-friendly formulation of quantum backflow compares to the standard one when applied to a free particle in a positive-momentum state. We show that the two formulations are not always compatible. We further identify a parametric regime in which the two formulations appear to be in qualitative agreement with one another.
Quantum backflow is a counterintuitive phenomenon in which the probability density of a quantum particle propagates opposite to its momentum. Experimental observation of backflow has remained elusive due to two main challenges: (i) the effect is intrinsically small, with less than 4% of the probability able to flow backward, and (ii) it requires wave packets with a well-defined momentum direction, which are difficult both to prepare and to verify under realistic, noisy conditions. Here, we overcome these challenges by introducing a general formulation of quantum backflow applicable to arbitrary momentum distributions. The framework recovers the standard backflow limit for unidirectional states and identifies general backflow as probability flow exceeding that predicted by the particle's momentum distribution alone. We show that this excess can reach nearly 13%, surpassing the standard backflow bound by more than a factor of three. Furthermore, we extend the framework to the closely related phenomenon of quantum reentry, provide explicit examples of quantum states exhibiting large general backflow and reentry, and discuss the foundational implications of these nonclassical effects. Our results open a pathway toward the experimental observation of quantum backflow in realistic settings.