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Journal of Physics B Atomic Molecular and Optical Physics

Cooperative emission spectra as an efficient key probe of qubits pair entanglement along with field state tomography: an effective response to nonlinearity and classical drive power

M. S. Ateto

Published Apr 15, 2020• 4 citations
Publisher

Abstract

Abstract Cooperative atomic emission spectrum as a key probe of entanglement dynamics of an independent and a classically-pumped qubits pair is showed and investigated. The qubits are initially maximally-entangled while they penetrate a detuned, single-photon and coherent cavity embedded in nonlinear media. The system Hamiltonian; that is a nonlinear and a time-dependent system, is diagonalized and the time evolution unitary operator in an exact form is derived. Various characteristics are monitored while observations are theoretically documented—via tracing the field state tomography—and experimentally calibrated. Cooperation and decoherence as well as the statistics of the emitted radiation are discussed and analyzed in terms of the other phenomena. We show that, a measurement of the spectrum outputs represent a highly effective key calibration for entanglement attributes, where complete time dynamics may be predicted with a high considerable accuracy. The most striking feature realized is that, on high detuned interaction, a full matching of these phenomena outputs can be achieved regardless of the absence or presence or pumping. Once the pumping starts, a partial dephasing is encouraged, thus, the spectrum is inversely but slightly affected, nevertheless, matching remains highly closed. Within various surroundings of Kerr materials of different Kerr constants, that is an additional source of an effective dephasing, spectrum rapidly oscillates and so also entanglement that shows rapid Rabi oscillations during its fast degradation depending on the detuning width. However, on measuring the intracavity field state tomography, measurements confirm such a matching, that is, calibration is well documented.

DOI
10.1088/1361-6455/ab8948

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Abstract Cooperative atomic emission spectrum as a key probe of entanglement dynamics of an independent and a classically-pumped qubits pair is showed and investigated. The qubits are initially maximally-entangled while they penetrate a detuned, single-photon and coherent cavity embedded in nonlinear media. The system Hamiltonian; that is a nonlinear and a time-dependent system, is diagonalized and the time evolution unitary operator in an exact form is derived. Various characteristics are monitored while observations are theoretically documented—via tracing the field state tomography—and experimentally calibrated. Cooperation and decoherence as well as the statistics of the emitted radiation are discussed and analyzed in terms of the other phenomena. We show that, a measurement of the spectrum outputs represent a highly effective key calibration for entanglement attributes, where complete time dynamics may be predicted with a high considerable accuracy. The most striking feature realized is that, on high detuned interaction, a full matching of these phenomena outputs can be achieved regardless of the absence or presence or pumping. Once the pumping starts, a partial dephasing is encouraged, thus, the spectrum is inversely but slightly affected, nevertheless, matching remains highly closed. Within various surroundings of Kerr materials of different Kerr constants, that is an additional source of an effective dephasing, spectrum rapidly oscillates and so also entanglement that shows rapid Rabi oscillations during its fast degradation depending on the detuning width. However, on measuring the intracavity field state tomography, measurements confirm such a matching, that is, calibration is well documented.
Entanglement dynamics of two identical non-interacting atoms (qubits) coupled individually with simultaneous classical and quantum fields are studied. The cavity field is filled with a nonlinear Kerr medium and initially prepared in a coherent state. The atoms are initially set up as a Bell-like pure state (BS). We present an approach for diagonalization of time-dependent nonlinear Hamiltonian of the system exactly. Connection between the change in the degree of entanglement and tomography of field state in phase space are also illustrated and interpreted. We demonstrate the possibility of atom–atom (qubit–qubit) entanglement optimization by suitably choosing initial interaction settings. Overall, we show that both classical driving amplitude and detuning as well as Kerr media and initial atomic states acts as the control parameters for the qubit–qubit entanglement. By adjusting of these parameters, accurately, entanglement can be enhanced noticeably and high degree of steady periodical entanglement can be generated. Moreover, starting with initial atomic BSs in presence of classical driving suppresses coherences randomness and considerably accompanied with (for specific values of detuning) slight decrease in their amplitudes. Furthermore, the addition of cross Kerr term suppresses degree of entanglement noticeably, where entanglement creation and enhancement could just be possible if cross Kerr effect is moved out from interaction. Our present approach promises the great advantage of being suitable for large quantum systems of various kinds of nonlinearities.
Waveguide quantum electrodynamics studies photon-mediated interactions of quantum emitters in a one-dimensional radiation channel. Although signatures of such interactions have been observed previously in a variety of physical systems, observation of coherent cooperative dynamics has been obscured by radiative decay of atoms into the waveguide. Employing transmon qubits as artificial atoms coupled to a microwave coplanar waveguide, here we observe dynamical oscillations in an open system where a designated probe qubit interacts with an entangled dark state of an array of qubits which effectively traps radiation as an atomic cavity. The qubit-cavity system is shown to achieve a large cooperativity of C=172 due to collective enhancement of photon-mediated interactions, entering the strong coupling regime. The quantum coherence of the dark state cavity is also explored through its nonlinear response at the single-excitation level. With realistic refinements, this system is suitable for studying the many-body dynamics of large (N>10) quantum spin chains, synthesizing highly non-classical radiation fields on demand, and implementing universal quantum logic operations with high fidelity on information encoded within decoherence-free subspaces.
In this paper, we explore the atomic population inversion and entanglement dynamics of a quantum system consisting of three identical two-level atoms interacting with a single-mode cavity field. The cavity is surrounded by a Kerr medium exhibiting f-deformed Kerr nonlinearity, and we consider a degenerate multi-photon transition in the nonlinear regime. The study systematically analyzes the effects of intensity-dependent coupling, detuning, Kerr nonlinearity, f-deformed Kerr nonlinearity, and multi-photon transition on the nonclassical properties of the system. Our results show that the Kerr and f-deformed Kerr nonlinearities significantly influence the atomic inversion dynamics, leading to phenomena such as collapse and revival, with distinct behaviors observed under varying detuning parameters. Furthermore, entanglement dynamics between the atoms and cavity mode are enhanced under intensity-dependent coupling and nonlinearity. The detuning parameter generally reduces entanglement but has a less pronounced effect in the two-photon transition case, where entanglement is notably enhanced. The study provides valuable insights into controlling quantum correlations in multi-atom systems, with potential applications in quantum information processing, computing, and communication.
The engineering of Kerr and time-dependent coupling interactions is of great attention for treating quantum information in quantum systems and for investigating the collective behavior of large numbers of interacting particles in a cavity-qubit network. In this manuscript, we investigate the time evolution of the entanglement and some nonclassical properties of two superconducting qubits interacting with a single-mode field in the presence of a Kerr-like medium and dipole–dipole interaction without and with time-dependent coupling effect. We show that a slight alteration in the interaction, detuning, and Kerr parameters might cause a change in the entanglement of subsystem states during the evolution. By taking into account the influence of the different physical parameters, we show the statistical distributions produced in the photons of the single mode field through the calculation of the Mandel’s parameter. Finally, we find that the time-dependent Mandel’s parameter not only provide the statistical properties of the field, but also include the information of quantum entanglement for the subsystem states.
Waveguide quantum electrodynamics studies photon-mediated interactions of quantum emitters in a one-dimensional radiation channel. Although signatures of such interactions have been observed previously in a variety of physical systems, observation of coherent cooperative dynamics has been obscured by radiative decay of atoms into the waveguide. Employing transmon qubits as artificial atoms coupled to a microwave coplanar waveguide, here we observe dynamical oscillations in an open system where a designated probe qubit interacts with an entangled dark state of an array of qubits which effectively traps radiation as an atomic cavity. The qubit-cavity system is shown to achieve a large cooperativity of C=172\mathcal{C}=172C=172 due to collective enhancement of photon-mediated interactions, entering the strong coupling regime. The quantum coherence of the dark state cavity is also explored through its nonlinear response at the single-excitation level. With realistic refinements, this system is suitable for studying the many-body dynamics of large (N>10N>10N>10) quantum spin chains, synthesizing highly non-classical radiation fields on demand, and implementing universal quantum logic operations with high fidelity on information encoded within decoherence-free subspaces.
We analyze the time-dependent physical spectrum of a driven Jaynes-Cummings model in which both the two-level system and the quantized cavity mode are subject to coherent classical driving. The time-dependent Hamiltonian is mapped, via well-defined unitary transformations, onto an effective stationary Jaynes-Cummings form. Within this framework, we derive closed-form expressions for the two-time correlation functions of both the atomic and field operators. These correlation functions are subsequently used to evaluate the time-dependent physical spectrum according to the Eberly-Wódkiewicz definition, which properly accounts for finite spectral resolution and transient emission dynamics. We show that the external driving leads to substantial modifications of the atomic spectral response, including controllable frequency shifts and asymmetric line shapes. Importantly, we identify a regime in which the driving parameters are chosen such that the coherent displacement induced in the cavity field exactly cancels out the initial coherent amplitude. In this limit, the system dynamics reduce to that of an effectively vacuum-initialized Jaynes-Cummings model, and the standard vacuum Rabi splitting is recovered. This behavior provides a clear and physically transparent interpretation of the spectral features as arising from coherent field displacement rather than from modifications of the underlying atom-cavity coupling.