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arXiv:2606.20278

Proposal of quantum arrival-time measurement with a Bose-Einstein condensate

Pascal Naidon, Lucas Happ, Denis Boiron

quant-phcond-mat.quant-gasSubmitted Jun 18, 2026• Announced Jun 19, 2026• 0 citations
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Abstract

This work shows how a Bose-Einstein condensate of ultracold atoms could be used to address a long-standing question in quantum theory: how much time does it take for a particle to reach a detector? To this end, we propose a realistic experimental setup, whose key idea is not to measure arrival times directly, but the arrival flux on the detector as a function of its position. This novel approach not only solves practical issues with having a detector close to the system, but also results in signals that allow to unambiguously distinguish different theoretical predictions. This proposal raises prospects for resolving the decades-old debate on this fundamental issue.

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8 pages ; 8 figures

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This work shows how a Bose-Einstein condensate of ultracold atoms could be used to address a long-standing question in quantum theory: how much time does it take for a particle to reach a detector? To this end, we propose a realistic experimental setup, whose key idea is not to measure arrival times directly, but the arrival flux on the detector as a function of its position. This novel approach not only solves practical issues with having a detector close to the system, but also results in signals that allow to unambiguously distinguish different theoretical predictions. This proposal raises prospects for resolving the decades-old debate on this fundamental issue.
The times of flight of an atomic Bose-Einstein condensate are theoretically investigated in the experimentally unexplored regime corresponding to detection close to the trap of the condensate. In this regime, there is no consensus on how to calculate the distribution of times of arrival onto the detector. For non-interacting particles, distinct theoretical predictions have been made in the past. This work analyses how these predictions are modified for an interacting Bose-Einstein condensate. For this purpose, a time-dependent Gross-Pitaevskii equation is solved analytically and numerically.
The problem of making unambiguous probabilistic predictions about experiments involving waiting "always on" detectors remains a challenge for quantum theory. While most research on this problem studies arrival time, i.e., predicting the distribution of when detection events occur, this paper studies the arrival position problem, which is the complementary challenge of predicting the distribution of where detection events occur. Despite the widespread recognition of the arrival time problem, the inability of standard quantum theory to address the arrival position problem remains a pervasive theoretical blind spot. In this paper, we compare quantitative arrival position predictions derived from prominent proposed solutions to the screen problem. As we show, these models yield distinguishable predictions even in relatively simple experiments achievable with current technology. Notably, many of these discrepancies persist even in the far-field limit, where standard semiclassical approximations are typically assumed to be valid.
What is the right statistics for the measurements of arrival times of a quantum particle? Although this question is very old, it is still open. The usual experiments are performed in the far-field regime and this question becomes unimportant, as a semiclassical analysis suffices. Nevertheless, the development in the detector technology will soon allow for near-field investigations; thus, a better understanding of arrival time measurements is needed. Since outcomes of quantum measurements are always described by positive-operator-valued measures (POVMs), various arrival time POVMs have been proposed. On the other hand, many physicists would agree that the arrival time statistics is given by the quantum flux. This urges the question whether a POVM exists, which agrees approximately with the quantum flux values on a reasonable set of wave functions. We answer this question negatively for a very natural set of wave functions, but we remark that the answer is very sensitive to the choice of the set and provide evidence for the existence of a POVM that agrees with the quantum flux on a more restrictive set.
Tunnelling is one of the phenomena at the heart of quantum mechanics. Despite its central role in physics, the duration of the tunnelling process has been debated since the development of quantum theory without a definite answer. In this thesis, the question of how long a particle takes to tunnel is investigated experimentally using ultracold atoms. These systems provide an ideal platform to address this question due to their isolation from the external environment and the ability to create almost arbitrary potentials for the atoms. As the tunnelling time experiment requires low temperatures, the realization and characterization of wave packets below the nanokelvin regime are studied first. A 16x reduction of the effective temperature of the atoms is obtained through delta-kick cooling. However, the achieved temperatures are so low that a new method, dubbed the “knife-edge technique”, is developed to characterize the final atomic state accurately. Through this new method, a final temperature of 900 ± 200 pK is found. Finally, the tunnelling time is investigated using a Bose-Einstein condensate in a one dimensional waveguide intersected by a 1.3 μm barrier. As the atoms tunnel through the thin potential, their spins time the tunnelling event through the Larmor precession induced by a pseudo-magnetic field localized inside the barrier. The precession angle is found by performing tomography on the spin state of the tunnelling atoms. With the knowledge of the Larmor frequency and the rotation angles, we find a tunnelling time of 0.65(7) ms. This experiment achieves a long-sought tunnelling time measurement with a clear interpretation, and its results show good quantitative agreement with theory based on the weak measurement formalism.
Temporal coherence is a fundamental property of macroscopic quantum systems, such as lasers in optics and Bose-Einstein condensates in atomic gases and it is a crucial issue for interferometry applications with light or matter waves. Whereas the laser is an ``open'' quantum system, ultracold atomic gases are weakly coupled to the environment and may be considered as isolated. The coherence time of a condensate is then intrinsic to the system and its derivation is out of the frame of laser theory. Using quantum kinetic theory, we predict that the interaction with noncondensed modes gradually smears out the condensate phase, with a variance growing as At2+Bt+C\mathcal{A}{t}^{2}+\mathcal{B}t+\mathcal{C}At2+Bt+C at long times ttt, and we give a quantitative prediction for A\mathcal{A}A, B\mathcal{B}B, and C\mathcal{C}C. Whereas the coefficient A\mathcal{A}A vanishes for vanishing energy fluctuations in the initial state, the coefficients B\mathcal{B}B and C\mathcal{C}C are remarkably insensitive to these fluctuations. The coefficient B\mathcal{B}B describes a diffusive motion of the condensate phase that sets the ultimate limit to the condensate coherence time. We briefly discuss the possibility to observe the predicted phase spreading, also including the effect of particle losses.