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Initial-Phase Spectroscopy as a Control of Entangled Systems

Levente Horvath, Z. Ficek

Published Aug 17, 2016• 2 citations
OpenAlex

Abstract

We introduce the concept of initial-phase spectroscopy as a control of the dynamics of entangled states encoded into a two-atom system interacting with a broadband squeezed vacuum field. We illustrate our considerations by examining the transient spectrum of the field emitted by two systems, the small sample (Dicke) and the spatially extended (non-Dicke) models. It is found that the shape of the spectral components depends crucially on the relative phase between the initial entangled state and the squeezed field. We follow the temporal evolution of the spectrum and show that depending on the relative phase a hole burning can occur in one of the two spectral lines. We compare the transient behavior of the spectrum with the time evolution of the initial entanglement and find that the hole burning can be interpreted as a manifestation of the phenomenon of entanglement sudden death. In addition, we find that in the case of the non-Dicke model, the collective damping rate may act like an artificial tweezer that rotates the phase of the squeezed field.

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Physical Review A•Oct 1, 1988•80 citations
We introduce the concept of initial-phase spectroscopy as a control of the dynamics of entangled states encoded into a two-atom system interacting with a broadband squeezed vacuum field. We illustrate our considerations by examining the transient spectrum of the field emitted by two systems, the small sample (Dicke) and the spatially extended (non-Dicke) models. It is found that the shape of the spectral components depends crucially on the relative phase between the initial entangled state and the squeezed field. We follow the temporal evolution of the spectrum and show that depending on the relative phase a hole burning can occur in one of the two spectral lines. We compare the transient behavior of the spectrum with the time evolution of the initial entanglement and find that the hole burning can be interpreted as a manifestation of the phenomenon of entanglement sudden death. In addition, we find that in the case of the non-Dicke model, the collective damping rate may act like an artificial tweezer that rotates the phase of the squeezed field.
We introduce the concept of initial-phase spectroscopy as a control of the dynamics of entangled states encoded into a two-atom system interacting with a broadband squeezed vacuum field. We illustrate our considerations by examining the transient spectrum of the field emitted by two systems, the small sample (Dicke) and the spatially extended (non-Dicke) models. It is found that the shape of the spectral components depends crucially on the relative phase between the initial entangled state and the squeezed field. We follow the temporal evolution of the spectrum and show that depending on the relative phase a hole burning can occur in one of the two spectral lines. We compare the transient behavior of the spectrum with the time evolution of the initial entanglement and find that the hole burning can be interpreted as a manifestation of the phenomenon of entanglement sudden death. In addition, we find that in the case of the non-Dicke model, the collective damping rate may act like an artificial tweezer that rotates the phase of the squeezed field.
Dynamics of entangled states of two independent single-mode cavities in squeezed reservoirs is investigated in the context of matching of the correlations contained in the entangled states to those contained in the squeezed reservoir. We illustrate our considerations by examining the time evolution of entanglement of single and double excitation NOON and EPR states. A comparison is made when each cavity is coupled to own reservoir or both cavities are coupled to a common reservoir. It is shown that the evolution of the initial entanglement and transfer of entanglement from the squeezed reservoir to the cavity modes depend crucially on the matching of the initial correlations to that contained in the squeezed reservoir. In particular, it is found that initially entangled modes with correlations different from the reservoir correlations prevent the transfer of the correlations from the squeezed field to the modes. In addition, we find that the transient entanglement exhibits several features unique to quantum nature of squeezing. In particular, we show that in the case of separate squeezed reservoirs a variation of the decay time of the initial entanglement with the squeezing phase is unique to quantum squeezing. In the case of a common reservoir a recurrence of entanglement occurs and we find that this feature also results from the reservoir correlations unique to quantum squeezing. There is no revival of entanglement when the modes interact with a classically squeezed field.
Dynamics of entangled states of two independent single-mode cavities in a correlated (squeezed) reservoir are investigated in the context of matching the correlations contained in the entangled states to those contained in the reservoir. We illustrate our considerations by examining the time evolution of entanglement of initial single and double excitation NOON and EPR states, and a comparison is made of when each cavity is coupled to its own reservoir or both cavities are coupled to a common reservoir. It is shown that the evolution of the initial entanglement and transfer of entanglement from the squeezed reservoir to the cavity modes depend crucially on the matching of the initial correlations to those contained in the squeezed reservoir. In particular, it is found that initially entangled modes with correlations different from the reservoir correlations prevent the transfer of the correlations from the squeezed field to the modes. In addition, we find that the transient entanglement exhibits several features unique to the quantum nature of squeezing. In particular, we show that in the case of separate squeezed reservoirs the initial entanglement disappears at a finite time, which for the so-called classically squeezed field remains almost the same as in the case of a thermal field. In the case of a common reservoir a recurrence of entanglement occurs and we find that this feature also results from the reservoir correlations unique to quantum correlations. There is no revival of the entanglement when the modes interact with a classically correlated field.
An investigation is reported of the collective effects and the dynamics of atom–atom entanglement in a system of two distant two-level atoms which are coupled via an optical element. In the system under consideration, the two atoms, which are trapped in the foci of a lens, are coupled to a common environment being in the vacuum state and they emit photons spontaneously. A fraction of the emitted photons from each atom is thus focused on the position of the other atom. The presence of optical element between two distant atoms leads to the occurrence of delayed collective effects, such as delayed dipole–dipole interaction and delayed collective spontaneous emission, which play the crucial role in the dynamical behaviour of the entanglement. We discuss the phenomena of entanglement sudden birth, entanglement sudden death, and revival of entanglement for both cases of initial one-photon and initial two-photon unentangled atomic states. We show that the evolution of the entanglement is sensitive not only to the interatomic distance but also to the initial state of the system as well as to the properties of the optical element.
Entanglement plays a crucial role in quantum information protocols; thus the dynamical behavior of entangled states is of great importance. In this paper, we suggest a useful scheme that permits a direct measure of entanglement in a two-qubit cavity system. It is realized through cavity-QED technology utilizing atoms as flying qubits. To quantify entanglement we use the concurrence. We derive the conditions that ensure that the state remains entangled in spite of the interaction with the reservoir. The phenomenon of entanglement sudden death in a bipartite system subjected to a squeezed vacuum reservoir is examined. We show that the sudden death time of the entangled states depends on the initial preparation of the entangled state and the parameters of the squeezed vacuum reservoir.
We have investigated the interaction of a single atom with a single mode of the radiation field in an ideal cavity when the field is initially in a squeezed-vacuum state. In particular, we present results for the spectrum of the emitted light and for the time evolution of the squeezing inside the cavity. Our results contrast sharply with previous studies of single two-level atom interaction with a continuum of squeezed-vacuum modes. In particular, the results are shown to be insensitive to the initial phase of the atomic dipole relative to the squeezed field, and the squeezing is destroyed by the coherent interaction, in a time essentially independent of the initial degree of squeezing. Most features of the spectrum are very similar to those predicted for an initial thermal state, although the two-peaked structure associated with vacuum-field Rabi splitting is more apparent for a squeezed state with a small average number of photons than for a thermal state with the same number of photons.