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Acta Physica Sinica

Squeezing and evolution of single particle by frequency jumping in two-dimensional rotating harmonic

Yu Wang, Yi-Hao Wu, Y. C. Li, Kai-Xiang Lu, Tian-Cheng Yi, Yunbo Zhang

Published Jan 1, 2024• 0 citations
Publisher

Abstract

The control of microscopic particle behavior based on a specific external field has always been a research hotspot in the field of physics. Many studies have been exploring various methods to manipulate and control the behavior of particles at a microscopic level. In this work, we investigate the phenomenon of single-particle squeezing induced by frequency jumping in a two-dimensional rotating harmonic oscillator potential. Squeezing, as a quantum mechanical phenomenon, has attracted significant attention due to its potential applications in various fields. It refers to the reduction of fluctuations in certain physical quantities, allowing for more precise measurement results. Squeezing phenomena have been extensively studied in different physical systems, including optics, atomic physics, and solid-state physics. However, there have been few reports on the quantum state squeezing phenomenon induced by frequency jumping in a rotating harmonic oscillator potential. Therefore, our study aims to fill this gap and shed light on this intriguing phenomenon. To explore the squeezing phenomenon induced by frequency jumping, we focus on the fluctuations and squeezing of the single particle’s cyclotron radius coordinate and center-guided coordinate in the two-dimensional rotating harmonic oscillator potential. Through numerical simulations and theoretical analysis, we can understand the influence of frequency jumping on the degree of squeezing and reveal the underlying physical mechanism of squeezing evolution. In this work, we first investigate the influence of frequency jumping on the squeezing evolution of the cyclotron radius mode. By carefully selecting appropriate jumping moments, we analyze the influence of frequency jumping on the degree of squeezing. Our research results show that the degree of squeezing in the cyclotron radius coordinate remains unchanged at the jumping moment. However, we observe a stronger squeezing phenomenon in the subsequent evolution process. This indicates that frequency jumping plays a crucial role in squeezing evolution of the cyclotron radius mode. Furthermore, we focus on the squeezing evolution of the center-guided mode during frequency jumping. By selecting suitable parameters, we analyze the squeezing and evolution of two squeezing modes: the divergent mode and the oscillatory mode. Interestingly, we discover the existence of a critical potential trap aspect ratio, which is determined by the rotation angular velocity of the external potential. When the aspect ratio approaches this critical value, the squeezing mode undergoes a transition, and a significant squeezing phenomenon appears in the oscillatory mode. This finding provides valuable insights into the origin and control of squeezing phenomena. Finally, we discuss the potential applications of these squeezing phenomena. Squeezing has significant implications in the fields of quantum sensing and quantum information processing. Through a deeper understanding of the squeezing evolution process caused by frequency jump, we can better control the microscopic particle behavior through external field. This knowledge opens up new possibilities for future physical research and technical applications.

DOI
10.7498/aps.73.20231929

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The control of microscopic particle behavior based on a specific external field has always been a research hotspot in the field of physics. Many studies have been exploring various methods to manipulate and control the behavior of particles at a microscopic level. In this work, we investigate the phenomenon of single-particle squeezing induced by frequency jumping in a two-dimensional rotating harmonic oscillator potential. Squeezing, as a quantum mechanical phenomenon, has attracted significant attention due to its potential applications in various fields. It refers to the reduction of fluctuations in certain physical quantities, allowing for more precise measurement results. Squeezing phenomena have been extensively studied in different physical systems, including optics, atomic physics, and solid-state physics. However, there have been few reports on the quantum state squeezing phenomenon induced by frequency jumping in a rotating harmonic oscillator potential. Therefore, our study aims to fill this gap and shed light on this intriguing phenomenon. To explore the squeezing phenomenon induced by frequency jumping, we focus on the fluctuations and squeezing of the single particle’s cyclotron radius coordinate and center-guided coordinate in the two-dimensional rotating harmonic oscillator potential. Through numerical simulations and theoretical analysis, we can understand the influence of frequency jumping on the degree of squeezing and reveal the underlying physical mechanism of squeezing evolution. In this work, we first investigate the influence of frequency jumping on the squeezing evolution of the cyclotron radius mode. By carefully selecting appropriate jumping moments, we analyze the influence of frequency jumping on the degree of squeezing. Our research results show that the degree of squeezing in the cyclotron radius coordinate remains unchanged at the jumping moment. However, we observe a stronger squeezing phenomenon in the subsequent evolution process. This indicates that frequency jumping plays a crucial role in squeezing evolution of the cyclotron radius mode. Furthermore, we focus on the squeezing evolution of the center-guided mode during frequency jumping. By selecting suitable parameters, we analyze the squeezing and evolution of two squeezing modes: the divergent mode and the oscillatory mode. Interestingly, we discover the existence of a critical potential trap aspect ratio, which is determined by the rotation angular velocity of the external potential. When the aspect ratio approaches this critical value, the squeezing mode undergoes a transition, and a significant squeezing phenomenon appears in the oscillatory mode. This finding provides valuable insights into the origin and control of squeezing phenomena. Finally, we discuss the potential applications of these squeezing phenomena. Squeezing has significant implications in the fields of quantum sensing and quantum information processing. Through a deeper understanding of the squeezing evolution process caused by frequency jump, we can better control the microscopic particle behavior through external field. This knowledge opens up new possibilities for future physical research and technical applications.
Two-mode squeezed states, which are entangled states with bipartite quantum correlations in continuous-variable systems, are crucial in quantum information processing and metrology. Recently, continuous-variable quantum computing with the vibrational modes of trapped atoms has emerged with significant progress, featuring a high degree of control in hybridizing with spin qubits. Creating two-mode squeezed states in such a platform could enable applications that are only viable with photons. Here, we experimentally demonstrate two-mode squeezed states by employing atoms in a two-dimensional optical lattice as quantum registers. The states are generated by a controlled projection conditioned on the relative phase of two independent squeezed states. The individual squeezing is created by sudden jumps of the oscillators' frequencies, allowing generating of the two-mode squeezed states at a rate within a fraction of the oscillation frequency. We validate the states by entanglement steering criteria and Fock state analysis. Our results can be applied in other mechanical oscillators for quantum sensing and continuous-variable quantum information.
Constructing and manipulating quantum states in fast-rotating Bose-Einstein condensates (BEC) has long stood as a significant challenge as the rotating speed approaching the critical velocity. Although the recent experiment [Science, 372, 1318 (2021)] has realized the geometrically squeezed state of the guiding-center mode, the remaining degree of freedom, the cyclotron mode, remains unsqueezed due to the large energy gap of Landau levels. To overcome this limitation, in this paper, we propose a Floquet-based state-preparation protocol by periodically driving an anisotropic potential. This protocol not only facilitates the single cyclotron-mode squeezing, but also enables a two-mode squeezing. Such two-mode squeezing offers a richer set of dynamics compared to single-mode squeezing and can achieve wavepacket width well below the lowest Landau level limit. Our work provides a highly controllable knob for realizing diverse geometrically squeezed states in ultracold quantum gases within the quantum Hall regime.
The frequency of a quantum harmonic oscillator cannot be precisely determined through static measurement strategies on a prepared state. Therefore, dynamical procedures must be employed, involving measurements taken after the system has evolved and encoded the frequency information. This paper explores the precision achievable in a protocol where a known detuning suddenly shifts the oscillator’s frequency, which then reverts to its original value after a specific time interval. Our results demonstrate that the squeezing induced by this frequency jump can effectively enhance the encoding of frequency information, significantly improving the quantum signal-to-noise ratio (QSNR) compared to standard free evolution at the same resource (energy and time) cost. The QSNR exhibits minimal dependence on the actual frequency and increases with both the magnitude of the detuning and the overall duration of the protocol. Furthermore, incorporating multiple frequency jumps into the protocol could further enhance precision, particularly for lower frequency values.
The quantum oscillator model plays a significant role in quantum optics and quantum information and has been one of the hot topics in related research fields. Inspired by the single-mode linear harmonic oscillator and the two-mode entangled state representation, we construct a two-mode coupled harmonic oscillator in this work. Different from the quantum transformation method used in previous literature, the entangled state representation is directly used in this work to solve its energy eigenvalues and eigenfunctions easily. The energy eigenvalues and eigenfunctions of this two-mode coupled harmonic oscillator are continuous compared with those of the one-mode harmonic oscillator. Using the matrix theory of quantum operators, we derive the transformation and inverse transformation of the time evolution operator corresponding to the two-mode coupled harmonic oscillator. In addition, using the entangled state representation, the specific form of the time evolution of the two-mode vacuum state under the action of the oscillator is obtained. Through the analysis of quantum fidelity, it is found that the fidelity of the output quantum state decreases with the oscillator frequency increasing, and the fidelity eventually tends to zero with the increase of time. When analyzing the orthogonal squeezing properties of the output quantum state, this type of two-mode oscillator does not have the orthogonal squeezing effect, but it has a strong quantum dissipation effect instead. This conclusion is further verified by the quasi-probability distribution Q function of the quantum state phase space. Therefore, the two-mode coupled harmonic oscillator has a major reference value in quantum control such as quantum decoherence and quantum information transmission. Like the two-mode squeezed vacuum state, the photon distribution of the output quantum light field corresponding to the two-mode harmonic oscillator presents a super-Poisson distribution, and the photons exhibit a strong anti-bunching effect. Using the three-dimensional discrete plot of the photon number distribution, the super-Poisson distribution and quantum dissipation effect of the output quantum state are intuitively demonstrated. Finally, the SV, which is an entanglement criterion, is used to determine that the output quantum state has a high degree of entanglement. Further numerical analysis shows that the degree of entanglement increases with the action time and the oscillator frequency. In summary, the two-mode coupled harmonic oscillator constructed in this work can be used to prepare highly entangled quantum states through a complete quantum dissipation process. This provides theoretical support for experimental preparing quantum entangled states based on dissipative mechanisms.
Abstract We investigate the Gouy phase emerging from the time evolution of confined matter waves in a harmonic potential. Specifically, we analyze the quantum dynamics of a Gaussian wavepacket that exhibits position–momentum correlations. By tuning the parameters governing its evolution, we reveal intriguing effects, with a particular focus on squeezing. Notably, during the wavepacket evolution quantum spreading and squeezing processes emerge, giving rise to Gouy phase contributions of π / 4 rad , establishing a clear link between the Gouy phase and a purely quantum phenomenon. Furthermore, the interplay between wavepacket squeezing and one-dimensional spreading leads to a total Gouy phase accumulation of π / 2 rad in an oscillation period. Both squeezing and Gouy phase have individually proven valuable in state engineering and quantum metrology. By demonstrating a direct, controllable relationship between these two fundamental processes, our findings expand the realm of quantum-enhanced technologies, including quantum sensing and precision measurement.
Due to the lack of experimental evidence of the quantum nature of gravity, interest in phenomena at the interface of quantum mechanics and gravity is growing. In this thesis we study two possible phenomena: vacuum fluctuations and collapse models. In the case of the former, we study both electromagnetic and gravitational fields as the origin of the fluctuations. In both cases we study the effect of the fluctuations on massive particles in harmonic oscillator potentials using open quantum system methods. For both fields, the fluctuations result in a frequency shift of the oscillator and the generation of coherences. For the electromagnetic case, we assess the role of the long-wavelength and rotating-wave approximations and show that the magnitude of the frequency shift is dependent on both approximations. We estimate the magnitude of the shift using parameters from a single-electron cyclotron experiment. For fluctuations of the gravitational field, we find the dynamics of the particle is tied to the choice of position observable. We study the interaction of two massive particles considering two choices of position observable: (i) a frame-dependent coordinate separation and (ii) a frame-independent geodesic separation. We find in the case of free particles (i) leads to unitary dynamics but (ii) leads to dissipation. We also find in the case of particles coupled through a linear spring that the magnitude of the frequency shift is dependent on the position observable chosen. Finally, we consider another possible phenomena associated with quantum gravity, collapse models. Existing literature suggests that inverted harmonic potentials are a good choice for measuring the diffusion predicted in collapse modes. Furthermore, it has been shown that phonon counting techniques, along with Gaussian transformations, can in principle obtain the fundamental quantum Cram´er-Rao bound. We find the required squeezing to obtain this limit for an inverted harmonic oscillator.