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International Journal of Geometric Methods in Modern Physics

Pancharatnam phase control of atomic ensembles based on quantum memory effects in photonic cavities

Elsayed Barakat, Ibrahim L. El-Kalla, Mahmoud Abdel‐Aty

Published Jan 3, 2025• 0 citations
Publisher

Abstract

In this paper, we explore the manipulation and control of the Pancharatnam phase in atomic ensembles through the utilization of quantum memory effects. By analyzing the time evolution of the excited state population of [Formula: see text]-atoms within a single photonic cavity, we gain insights into the behavior and manipulation of this phase. Numerical simulations of the system exact solution yield density plots illustrating the time evolution of the excited state population and Pancharatnam phase. Our findings demonstrate the potential to control the system dynamics using the Pancharatnam phase in atomic ensembles through quantum memory effects. The observed behaviors and characteristics contribute to our understanding of quantum systems and hold promise for crucial applications in quantum information processing and communication. These results provide valuable insights into the fundamental aspects of the Pancharatnam phase and its control, paving the way for further investigations and applications in quantum optics and information science.

DOI
10.1142/s0219887825500975

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In this paper, we explore the manipulation and control of the Pancharatnam phase in atomic ensembles through the utilization of quantum memory effects. By analyzing the time evolution of the excited state population of [Formula: see text]-atoms within a single photonic cavity, we gain insights into the behavior and manipulation of this phase. Numerical simulations of the system exact solution yield density plots illustrating the time evolution of the excited state population and Pancharatnam phase. Our findings demonstrate the potential to control the system dynamics using the Pancharatnam phase in atomic ensembles through quantum memory effects. The observed behaviors and characteristics contribute to our understanding of quantum systems and hold promise for crucial applications in quantum information processing and communication. These results provide valuable insights into the fundamental aspects of the Pancharatnam phase and its control, paving the way for further investigations and applications in quantum optics and information science.
Quantum optics provides tools for the accurate control of light using atoms and also for manipulating atomic states using light. These techniques are being used for many applications, including quantum information processing and the generation of exotic quantum states. This thesis contains proposals for implementing a photonic quantum memory and a photon-photon gate, which are essential elements of photonic quantum information processing. Furthermore it proposes a scheme for the creation of many-body entangled states. First a proposal for a new quantum memory protocol, called the atomic frequency sweep quantum memory, is presented. A two-level polariton model is derived that explains the coherent storage and retrieval of light through the manipulation of the atomic resonance frequency. This is followed by a scheme for a deterministic photonic controlled-PHASE gate based on the strong interaction between two stationary collective Rydberg excitations in an atomic ensemble. Distortion effects caused by nonuniform interaction are quantified and compensation techniques for these effects are proposed. Finally a proposal is presented that uses Rydberg dressing for the generation of energy cat states in an atomic medium, i.e. superposition states of all the atoms being in the ground or excited state, where these two states are connected by an optical transition and thus have a significant difference in energy. Considering the fragility of the state, the effects of many different imperfections and decoherence sources are quantified. The resulting cat state would allow testing of energy decoherence models with greatly improved sensitivity.
Quantum information science and atom optics are among the most active fields in modern physics. In recent years, many theoretical efforts have been made to combine these two fields. Recent experimental progresses have shown the in-principle possibility to perform scalable quantum information processing (QIP) with linear optics and atomic ensembles. One of our main activities is to use atomic qubits as quantum memory and exploit photonic qubits for information transfer and processing to achieve efficient linear optics QIP. On the one hand, utilizing the interaction between laser pulses and ultra-cold atomic ensembles we experimentally investigate the potentials of atomic ensembles in the gas phase to build quantum repeaters for long-distance quantum communication, that is, to develop a new technological solution for quantum repeaters making use of the effective qubit-type entanglement of two cold atomic ensembles by a projective measurement of individual photons by spontaneous Raman processes.
Abstract We investigate the non-stationary and relaxation phenomena in cavity-assisted quantum memories for light. As a storage medium we consider an ensemble of cold atoms with standard Lambda-scheme of working levels. Some theoretical aspects of the problem were treated previously by many authors, and recent experiments stimulate more deep insight into the ultimate ability and limitations of the device. Since quantum memories can be used not only for the storage of quantum information, but also for a substantial manipulation of ensembles of quantum states, the speed of such manipulation and hence the ability to write and retrieve the signals of relatively short duration becomes important. In our research we do not apply the so-called bad cavity limit, and consider the memory operation of the signals whose duration is not much larger than the cavity field lifetime, accounting also for the finite lifetime of atomic coherence. In our paper we present an effective approach that makes it possible to find the non-stationary amplitude and phase behavior of strong classical control field, that matches the desirable time profile of both the envelope and the phase of the retrieved quantized signal. The phase properties of the retrieved quantized signals are of importance for the detection and manipulation of squeezing, entanglement, etc by means of optical mixing and homodyning.
Quantum information has been witnessing great science value and latent application since 1980's. The research work presented here consist of mainly two important parts: manipulations of multiphoton entanglement and atomic ensembles based quantum memory. In first part, the experimental technique multi-photon entanglement is further developed to study fundamental issues in quantum mechanics, remarkable applications to quantum communication and quantum computation. Specifically, we have demonstrated a bit-flip error-free transfer of quantum information, violation of Bell's inequality beyond Tsirelson's bound, teleportation of a two-qubit composite system, as well as the one-way computing by two-photon-four-qubit cluster state. To overcome un-scalability problem due to probabilistic feature in linear optical quantum information processing, we investigated in the second part the physics of atomic ensembles based quantum memory. We show that theoretically, entanglement between distant locations can be deterministically generated. The experimental work has thoroughly developed the necessary techniques and we have achieved deterministic single photon source, and interference of the photons from independent atomic ensembles, teleportation between photonic and atomic qubits, a novel way to create a robust entanglement between an atomic and a photonic qubit, and memory based entanglement swapping. We believe, the developed techniques here would dramatically facilitate progresses in many fields including global quantum communication, linear optical quantum computation and the foundations of quantum mechanics etc.
In this paper we consider a Hamiltonian modelling a pair of two-level atoms within a perfect cavity for the case of a two-photon transition. Under the exact resonance condition and in the presence of both the Stark shift and phase shift an exact solution to the Schrödinger equation is obtained. Employing this solution gives an analytical expression for the temporal evolution of the Pancharatnam phase when a second atom is allowed to interact with the cavity mode and becomes entangled with the first atom. Numerical investigations are carried out for the phenomena of collapses and revivals for different Stark shift values, the distance between the two atoms and the phase shift. It has been shown that the Pancharatnam phase is affected by the Stark shift and the distance between the two atoms when a nonlinear two-photon process is involved
Cold atomic ensembles and spinor Bose-Einstein condensates are potential candidates for quantum memories as they have long coherence times and can be coherently controlled. Unlike most candidates for quantum memories, which are genuine or effective single-particle systems, in atomic ensembles the quantum information is stored as a spin coherent state involving a very large number of atoms. A typical task with such ensembles is to drive the state towards a particular quantum state. While such quantum control methods are well developed for qubit systems, it is a nontrivial task to extend quantum control methods to the many-particle case. The objective of this work is to deterministically steer an arbitrary state of the atomic ensemble into a desired spin coherent state. To this end, we design our control law using stochastic stability theory, the quantum filtering theorem, and phase contrast imaging. We apply our control laws to different axes and show that it is possible to manipulate the atoms into different target states.