Core Concepts

Acceleration significantly alters the tunneling dynamics of bosons in a double-well potential, and these changes can be used to effectively measure the acceleration.

Abstract

The study investigates the impact of acceleration on the tunneling dynamics of bosons in a double-well (DW) potential. The authors explore both constant and time-dependent accelerations and analyze two key quantities: the survival probability in the left well (calculated from mean-field density) and the many-body depletion from the condensate.

For constant acceleration, the tunneling time period decreases exponentially with increasing acceleration, allowing for the assessment of larger accelerations. However, for smaller accelerations where the tunneling period is close to the Rabi oscillation time, this method becomes less reliable. To address this, the authors propose using the depletion as an alternative measure, which shows a linear decrease with increasing acceleration in the small acceleration regime.

The analysis is then extended to time-dependent accelerations, where the authors demonstrate that the tunneling time period and depletion can be used to effectively quantify the acceleration, even in more complex scenarios. Furthermore, the authors investigate small deviations from constant acceleration and constant velocity, showing that the depletion exhibits an exponential behavior for deviations from constant acceleration and a polynomial behavior for deviations from constant velocity.

Overall, the study establishes the bosonic Josephson junction as a versatile platform for assessing a wide range of accelerations, from large to small, by leveraging the tunneling dynamics and many-body depletion.

To Another Language

from source content

arxiv.org

Stats

The tunneling time period decreases exponentially with increasing acceleration.
The depletion at the Rabi time decreases linearly with increasing acceleration for small accelerations.

Quotes

"Acceleration significantly alters the tunneling dynamics of bosons in a double-well potential, and these changes can be used to effectively measure the acceleration."
"For constant acceleration, the tunneling time period decreases exponentially with increasing acceleration, allowing for the assessment of larger accelerations."
"To address this, the authors propose using the depletion as an alternative measure, which shows a linear decrease with increasing acceleration in the small acceleration regime."

Key Insights Distilled From

by Rhombik Roy,... at **arxiv.org** 10-01-2024

Deeper Inquiries

In higher-dimensional double-well potentials, the tunneling dynamics and acceleration assessment would exhibit more complex behavior compared to one-dimensional systems. The increased dimensionality introduces additional degrees of freedom for the bosonic particles, which can lead to richer tunneling phenomena, such as multi-channel tunneling and the possibility of anisotropic tunneling rates. The tunneling dynamics may become sensitive to the geometry of the potential wells, including the shape and orientation of the wells, which could affect the tunneling probabilities and the associated time periods.
Moreover, the assessment of acceleration in higher dimensions would require a more sophisticated analysis of the many-body depletion and survival probabilities. The interplay between the spatial distribution of particles and the acceleration could lead to non-trivial correlations that are not present in one-dimensional systems. For instance, the depletion dynamics might exhibit anisotropic behavior, where the depletion rate varies depending on the direction of acceleration. This complexity necessitates the development of advanced theoretical models and numerical simulations to accurately capture the dynamics in higher-dimensional settings.

The experimental implementation of acceleration measurement techniques using bosonic Josephson junctions (BJJs) faces several limitations and challenges. Firstly, achieving and maintaining ultracold temperatures necessary for the formation of Bose-Einstein condensates (BECs) is technically demanding. Any fluctuations in temperature can significantly affect the coherence and stability of the BEC, thereby impacting the tunneling dynamics and the accuracy of acceleration measurements.
Secondly, the precision of the measurement techniques relies heavily on the ability to control the parameters of the double-well potential, such as the depth and width of the wells, as well as the interaction strength between bosons. Any imperfections in the potential or variations in the interaction strength can introduce noise and systematic errors in the measurements.
Additionally, the sensitivity of the depletion measurement to small accelerations may be limited by the finite size of the BEC and the statistical fluctuations inherent in many-body systems. As the acceleration becomes very small, distinguishing the effects of acceleration from other noise sources becomes increasingly challenging.
Finally, the implementation of time-dependent accelerations adds another layer of complexity, as it requires precise control over the acceleration profile and the ability to measure the resulting tunneling dynamics in real-time. This necessitates advanced experimental setups and data acquisition systems capable of capturing rapid changes in the system's behavior.

Yes, the insights gained from this study on the interplay between acceleration and quantum tunneling can be extended to other quantum systems beyond bosonic Josephson junctions. The fundamental principles governing quantum tunneling and the effects of non-inertial reference frames are applicable to a wide range of quantum systems, including fermionic systems, quantum dots, and superconducting qubits.
For instance, in fermionic systems, similar tunneling dynamics can be observed, and the effects of acceleration could influence the coherence and entanglement properties of the system. The techniques developed for assessing acceleration through tunneling dynamics could be adapted to measure forces or accelerations in these systems, potentially leading to new applications in quantum metrology.
Moreover, the study's findings could inform research in quantum information processing, where understanding the effects of acceleration on tunneling dynamics may enhance the design of quantum gates and circuits. The principles of quantum tunneling in non-inertial frames could also be relevant in the context of gravitational effects on quantum systems, opening avenues for exploring the interplay between gravity and quantum mechanics.
Overall, the exploration of acceleration's impact on quantum tunneling in bosonic Josephson junctions provides a valuable framework that can be generalized to other quantum systems, enriching our understanding of quantum phenomena across various platforms.

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