Quantum qubit-optical cavity node: Effects of the temperature and coupling strengths on the cavity Fock-state distribution occupation probability and entropy of the subsystems using Dicke model
Mohamed Barhoumi, Riccardo Bassoli, Frank H. P. Fitzek
Abstract One of the most attractive systems for scalable quantum processing is the trapped atom in the optical cavity, which is easily manipulable with lasers. The qubit-cavity system represents an attractive structure for quantum optics, with possibilities for applications in quantum detecting, quantum computation, and quantum communication. Also, the investigation of the cavity-atom system under temperature is a fundamental concept in quantum optics and quantum information science. Here we continue in this quantum way, investigating different qubit(s)-cavity systems (where we increase the numbers of the qubit inside the optical cavity from one to four). Employing the Dicke model, we calculate the cavity ground state occupation probability ⟨â † ˆ a⟩ and the expectation values ⟨Jz⟩ for each system. We find that these probabilities increase when the coupling 1 strength Cs increases. This leads to reaching the ultra-strong coupling regime, which depends on the numbers of the qubits. To describe the quantum state, we examine the cavity Wigner function WF as a function of the coupling strength Cs. Under the same parameters (e.g., Cs and the dissipation rates), we obtain that the separation of the quantum state in the WFs representation is different from one system to another. Furthermore, since understanding these kinds of systems is very important in order to improve the quantum network system, we study the entropy S of the subsystems (like S of qubit) in each system. Also, we move beyond by studying the effect of the temperature on the Fock-state distribution occupation probability and entropy of the subsystems. Our outcomes present another step to understanding the qubit(s)-cavity interaction to improve the performance of the future quantum networks based on this system.
Abstract One of the most attractive systems for scalable quantum processing is the trapped atom in the optical cavity, which is easily manipulable with lasers. The qubit-cavity system represents an attractive structure for quantum optics, with possibilities for applications in quantum detecting, quantum computation, and quantum communication. Also, the investigation of the cavity-atom system under temperature is a fundamental concept in quantum optics and quantum information science. Here we continue in this quantum way, investigating different qubit(s)-cavity systems (where we increase the numbers of the qubit inside the optical cavity from one to four). Employing the Dicke model, we calculate the cavity ground state occupation probability ⟨â † ˆ a⟩ and the expectation values ⟨Jz⟩ for each system. We find that these probabilities increase when the coupling 1 strength Cs increases. This leads to reaching the ultra-strong coupling regime, which depends on the numbers of the qubits. To describe the quantum state, we examine the cavity Wigner function WF as a function of the coupling strength Cs. Under the same parameters (e.g., Cs and the dissipation rates), we obtain that the separation of the quantum state in the WFs representation is different from one system to another. Furthermore, since understanding these kinds of systems is very important in order to improve the quantum network system, we study the entropy S of the subsystems (like S of qubit) in each system. Also, we move beyond by studying the effect of the temperature on the Fock-state distribution occupation probability and entropy of the subsystems. Our outcomes present another step to understanding the qubit(s)-cavity interaction to improve the performance of the future quantum networks based on this system.
Atom-cavity interconnected systems offer an outstanding possibility for experiments in quantum computing and quantum information. Investigating the interaction between different light fields and atoms in a cavity is a vital study area of quantum optics. In this paper, we investigate the interaction between an atom(qubit) and the cavity. The Jaynes-Cummings approach is used to determine the probability of the cavity and qubit into bad and good regimes. Moreover, we examine the Wigner-functions of the cavity depending on the coupling strength. It is possible to synchronize atoms to create extremely precise atomic clocks, which might revolutionize several sectors, including navigation, communications, and scientific study. We show that the synchronization of two qubits inside an optical lattice can be accomplished using the driven Tavis-Cummings Hamiltonian. In this framework, we employ sixteen photons and show that the best quantum synchronization can be achieved between two qubits 𝑞1 and 𝑞2 in a weak regime.
The investigation of the dissipative qubit (atom) cavity system has opened up new possibilities for the development of quantum technology. Nevertheless, the understanding of this system is still poor. Also, the integration of qubit-cavity into 5G networks is still in its early stages, where the combination of 5G and quantum technology can revolutionize various sectors, including the Internet of Things IoT. Here we study a dissipative qubit-cavity quantum system, where we compute the time evolution of the excitation probabilities of the cavity and qubit as a function of the coupling strength and under the dissipation rates. To understand various processes, the study of the temperature in a cavity atom system is required. The time-evolution of the occupation probability of the cavity and qubit is achieved under different temperatures. Moreover, we examine the Wigner function at different times and under different temperatures. We demonstrate that the appearance of separation of the quantum state in WF representations depends on the coupling strength. The findings have important significance for quantum technology, including quantum information processing. Thus, we suggest an implementable schematic (network architecture based on the entangled photons) for explaining how to link cavities to a real 5G network. In this quantum route, we present a model of how time synchronization can be measured by employing quantum synchronization and integrating it into the existing 5G network.
We simulate the dynamics of systems with N = 1-20 qubits coupled to a cavity in order to assess their potential for quantum metrology of a parameter in the open systems limit. The qubits and the cavity are both allowed to have losses and the system is studied under various coupling strength regimes. The focus is primarily on the coupling between the qubits using the quantum Fisher information as the measured parameter. Some results on estimating the qubit-cavity detuning parameter are also presented. We investigate the scaling of the uncertainty in the estimate of the qubit-cavity coupling with the number of qubits and for different initial states of the qubits that act as the quantum probe. As initial probe states, we consider Dicke states with varying excitation numbers, the GHZ state, and separable X-polarized states. It is shown that in the strong coupling regime, i.e., when the coupling between the qubits and the cavity is greater than the decay parameters of both the qubits and the cavity, Dicke states with a large excitation number can achieve the Heisenberg limit, with the precision scaling improving as the excitation number increases. A particularly intriguing finding of our study is that in the weak coupling regime, as well as in situations where either the qubit or cavity decay parameters exceed the coupling, the separable X-polarized state is the best in terms of scaling and is even able to achieve the Heisenberg limit in these lossy regimes for the range of N considered.
Dicke model describes a collective interaction between the two-level atoms and the light cavity and has been predicted to show a peculiar quantum phase transition, which is a second-order phase transition from a normal phase (in a weak-coupling strength) to a superradiant phase (in a strong-coupling strength). The model plays an important role in illustrating the quantum ground-state properties of many-body macroscopic quantum states. In the experiment, Dicke quantum phase transition in an open system could be formed by a Bose-Einstein condensate coupled to a high-finesse optical cavity. This experiment on the Bose-Einstein condensate trapped in the optical cavity have opened new frontiers, which could combine the cold atoms with quantum optics and makes it possible to enter into the strongly coupled regime of cavity quantum electrodynamics. In strong coupled regime, the atoms exchange the photons many times before spontaneous emission and cavity losses set in. It has become a hot research topic in recent years and plays an important role in many fields of modern physics, such as condensed matter physics, nuclear physics, etc. It can be applied to the manipulation of the geometric phase and entanglement in quantum information and computing. Quantum phase transition has been widely studied for the Dicke model as a typical example. Many different research methods about the mean-field approximation have been used to analyze the ground state properties of the Dicke model. In this paper, we study the ground state properties of two-component Bose-Einstein condensate in a single-mode cavity. Meanwhile, the associated quantum phase transition is described by the spin-coherent-state variational method, whose advantage is that the ground state energy and wave function can be obtained without the thermodynamic limit. By taking the average in the boson coherent state, we obtain an equivalent effective pesudospin Hamiltonian, which will be diagonalized by using the spin coherent state. Finally, we can obtain the energy functional, which is the basics of the variation to obtain the numerical solution of photon number and the expression of the atomic number and the ground state energy. This paper presents a rich phase diagram, which can be manipulated by changing the atom-field coupling imbalance between two components and the atom-field frequency detuning. While in the single-mode Dicke model there exist only the normal phase and the superradiation phase. When the frequency of one component atom is zero or the frequency of the two component atoms are equal in optical cavity, the system returns to the standard Dicke model, in which there occurs the second-order phase transition from the normal phase to the superradiant phase by adjusting the atom-field coupling. In conclusion, we discover that the stimulated radiation comes from the collective state of atomic population inversion, which does not exist in the single-mode Dicke model. Meanwhile, the new stimulated-radiation state S and S, which can only be produced by one component of the atom, are observed in the two-component Bose-Einstein condensates in the single-mode optical cavity. By adjusting the atom-field coupling imbalance and the atom-field frequency detuning (the blue or red detuning), the order of the superradiation state and the stimulated-radiation states can be exchanged between the two components of the atom.
This thesis summarizes the research work we did in the past years, which focuses on the theoretical study of quantum effects of ordered atomic structures interacting with the quantum electric field of an optical resonator. Within this work we investigated the quantum properties of the light at the cavity output, emitted by this kind of system, and the quantum state of the atoms confined by the light fields of the cavity mode. Following one possible partition, we have organized the thesis in two parts. The first part of the thesis is devoted to the quantum properties of the light at the output of optical cavities, in which atoms are confined. After a brief introduction on the basics of atom-photon interactions, we show theoretically, that two atomic dipoles in a resonator can behave as a quantum non-linear medium, whose response can be controlled through the interactomic distance of the atoms inside the resonator. We identify the parameter regime, for which the system operates as a parametric amplifier, based on the atoms' collective dipole cascade emission. Moreover we also determine the corresponding field squeezing spectrum at the cavity output. These dynamics could be observed as a result of self-organization processes of laser-cooled atoms in resonators. The second part of the thesis studies the quantum ground state of an ultracold atomic gas trapped inside an optical resonator by the mechanical effects of atom-photon interactions. Due to the strong coupling regime, the ultracold atomic gas feels a quantum potential, where the fluctuations at the single photon level may be relevant in determining the trapping conditions. This potential depends on the atomic distribution, which at the same time determines the intracavity field amplitude. Here, after a brief introduction on ultracold atoms in optical lattices, we study the low temperature physics of an ultracold atomic gas in the quantum potential formed inside a pumped cavity, by mapping the dynamics to an effective Bose-Hubbard model. We predict the existence of non-compressible states of the atomic gas, and determine a phase diagram as a function of the cavity parameters. Novel effects are encountered, such as the existence of overlapping stability regions corresponding to competing insulator-like states when the laser pumps the cavity, to provide one example out of many. At the end of the thesis a concluding chapter presents some general outlooks to this thesis work.
The Dicke model describing an ensemble of two-state atoms interacting with a single quantized mode of the electromagnetic field (with omission of the ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A}}^{2}$ term) exhibits a zero-temperature phase transition at a critical value of the dipole coupling strength. We propose a scheme based on multilevel atoms and cavity-mediated Raman transitions to realize an effective Dicke model operating in the phase transition regime. Optical light from the cavity carries signatures of the critical behavior, which is analyzed for the thermodynamic limit where the number of atoms is very large.