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Journal of Physics Conference Series

Single-photon generation of entangled triplet state in an atomic spin dimer

S. K. Varbev, Iavor I. Boradjiev, Hassan Chamati

Published Feb 1, 2021• 0 citations
Publisher

Abstract

Abstract We show that the entanglement between two atomic spins, coupled via XY interaction, can be achieved with the aid of a single photon in a controllable manner. Assuming a constant spin-photon coupling, two distinct cases are considered — excitation with a constant and with a linear time-dependent photon frequency. We demonstrate that these problems reduce to the study of the well known Jaynes-Cummings and Jaynes-Cummings – Landau-Zener models, respectively, where the two-level system is formed by the zero-momentum mode states of the dimer. Owing to the exact solubility of both models, by tuning the relevant parameters, one can design and coherently control the dynamics of the excitation process. For instance, one can adiabatically switch from an atomic spin system initialized in a state with both spins down to the maximally entangled triplet state.

DOI
10.1088/1742-6596/1762/1/012015

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Abstract We show that the entanglement between two atomic spins, coupled via XY interaction, can be achieved with the aid of a single photon in a controllable manner. Assuming a constant spin-photon coupling, two distinct cases are considered — excitation with a constant and with a linear time-dependent photon frequency. We demonstrate that these problems reduce to the study of the well known Jaynes-Cummings and Jaynes-Cummings – Landau-Zener models, respectively, where the two-level system is formed by the zero-momentum mode states of the dimer. Owing to the exact solubility of both models, by tuning the relevant parameters, one can design and coherently control the dynamics of the excitation process. For instance, one can adiabatically switch from an atomic spin system initialized in a state with both spins down to the maximally entangled triplet state.
We analyze the problem of a single mode field interacting with a pair of two level atoms. The atoms enter and exit the cavity at different times. Instead of using constant coupling, we use time-dependent couplings which represent the spatial dependence of the mode. Although the system evolution is adiabatic for most of the time, a previously unstudied energy crossing plays a key role in the system dynamics when the atoms have a time delay. We show that conditional atom-cavity entanglement can be generated, while for large photon numbers the entangled system has a behavior which can be mapped onto the single atom Jaynes-Cummings model. Exploring the main features of this system we propose simple and fairly robust methods for entangling atoms independently of the cavity, for quantum state mapping, and for implementing SWAP and controlled-NOT (CNOT) gates with atomic qubits.
We describe a mathematical solution for the generation of entangled N-photon states in two field modes. A simple and compact solution is presented for a two-mode Jaynes-Cummings model by combining the two field modes in a way that only one of the two resulting quasimodes enters in the interaction term. The formalism developed is then applied to calculate various generation probabilities analytically. We show that entanglement, starting from an initial field and an atom in one defined state may be obtained in a single step. We also show that entanglement may be built up in the case of an empty cavity and excited atoms whose final states are detected, as well as in the case when the final states of the initially excited atoms are not detected.
New technologies providing tight focusing lens and mirrors with large numerical apertures and electro-optic modulation of single photons are now available for the investigation of photon-atom interactions without a cavity. From the theoretical side, new models must be developed which take into account the intrinsic open system aspect of the problem as well as details about atomic relative positions and temporal (spectral) features of the pulses. In this paper, we investigate the generation of nonclassical correlations between two atoms in response to their interaction with a quantized pulse containing just one single photon. For this purpose, we develop a general theoretical approach which allows us to find the equations of motion for single- and two-body atomic operators from which we obtained the system density operator. We show that one single photon is capable of generating substantial entanglement between the atoms, and we analyze the dependence of these correlations on atomic relative positions and spectral features of the pulse.
The interaction of a two-level cyclic XY n-spin model with a two-mode cavity field involving two-photon transitions is investigated through a generalized Jaynes-Cummings model in the rotating-wave approximation. The two-photon interacting Hamiltonian becomes from the replacement of each single-mode field in the one-photon interacting Hamiltonian with the second-harmonic generation. It was assumed that initially the correlated field modes are in disentangled coherent states having the same photon distribution and that the spin system is in an excited state. At any time t > 0, the spin system and the field are in an entangled state, in this case, via a unitary time evolution operator. Thus, the spontaneous decay of a spin level was treated by considering the interaction of the two-level spin system with the modes of the universe in the vacuum state. The different cases of interest, characterized in terms of a detuning parameter for each mode, which emerge from nonvanishing commutation relations, were analytically implemented and numerically discussed for various values of the initial mean photon number and spin-photon coupling constants. Photon distribution, time evolution of the spin population inversion, as well as the statistical properties of the field leading to the possible production of nonclassical states, such as antibunched light, violations of the Cauchy-Schwartz inequality, and second- and fourth-order squeezing, are examined. The case of zero detuning of both modes was treated in terms of a linearization of the expansion of the time evolution operator, while in other three cases, the computations were conducted via second- and third-order Dyson perturbation expansion of the time evolution operator matrix elements for the excited and ground states of the spin system, respectively.
In this paper, we study the interaction between the time-dependent field and a two-level atom with one mode electromagnetic field. We consider that the field of photons is assumed to be coupled with modulated coupling parameter which depends explicitly on time. It is shown that the considered model can be reduced to a well-known form of the time-dependent generalized Jaynes–Cummings model. Under special initial conditions, in which the atom and the field are prepared in the excited and the coherent states, respectively, the explicit time evolution of the wave function of the entire system is analytically obtained. Our proposal has many advantages over the previous optical schemes and can be realized in several multiple experiments, such as trapped ions and quantum electrodynamics cavity. The influence of the time-dependent field parameter on the collapses-revivals, the normal squeezing of the radiation, the anti-bunching of photons and the entanglement phenomena for the considered atomic system is examined. The linear entropy, the von Neumann entropy are used to quantify entanglement in the quantum systems. We noticed that these phenomena are affected by the existence of both the time-dependent coupling field and detuning parameters.
Entanglement between a single photon and a matter qubit is an indispensable resource for quantum repeater and quantum networks. With atomic ensembles, the entanglement creation probability is typically very low to inhibit high-order events. In this paper, we propose and experimentally realize a scheme that creates atom-photon entanglement with an intrinsic efficiency of 50%. We make use of Rydberg blockade to generate two collective excitations, lying in separate internal states. By introducing the momentum degree of freedom for the excitations, and interfering them via Raman coupling, we entangle the two excitations. Via retrieving one excitation, we create the entanglement between the polarization of a single photon and the momentum of the remaining atomic excitation, with a measured fidelity of 0.901(8). The retrieved optical field is verified to be genuine single photons. The realized entanglement may be employed to create entanglement between two distant nodes in a fully heralded way and with a much higher efficiency.