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Low Temperature Physics

Transfer of excited state between two qubits in an open waveguide

A. N. Sultanov, Ya. S. Greenberg

Published Mar 1, 2018• 4 citations
Publisher

Abstract

The probability amplitudes of the processes related to the transfer of the excited state from one qubit to another are calculated using an indirect interaction in an open waveguide. The system consists of two qubits located at an arbitrary distance from each other. The non-Hermitian effective Hamiltonian approach used herein makes it possible to bypass using the Markovchain approximation method. Analytic expressions describing the probability of transfer of the excited state from one qubit to another under different initial states of the system were obtained.

DOI
10.1063/1.5024536

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The probability amplitudes of the processes related to the transfer of the excited state from one qubit to another are calculated using an indirect interaction in an open waveguide. The system consists of two qubits located at an arbitrary distance from each other. The non-Hermitian effective Hamiltonian approach used herein makes it possible to bypass using the Markovchain approximation method. Analytic expressions describing the probability of transfer of the excited state from one qubit to another under different initial states of the system were obtained.
We investigate the propagation of microwave photons in a one-dimensional open waveguide interacting with a number of artificial atoms (qubits). Within the formalism of projection operators and a non-Hermitian Hamiltonian approach we develop a one-photon approximation scheme for the calculation of the transmission and reflection factors of the microwave signal in a waveguide which contains an arbitrary number NNN of noninteracting qubits. We considered in detail the resonances and photon-mediated entanglement for two and three qubits in a chain. We showed that in the non-Markovian case the resonance widths, which define the decay rates of the entangled state, can be much smaller than the decay width of an individual qubit. It is also shown that for identical qubits in the long-wavelength limit a coherent superradiant state is formed with the width being equal to the sum of the widths of spontaneous transitions of NNN individual qubits. The results obtained in the paper are of general nature and can be applied to any type of qubits. The specific properties of the qubit are only encoded in the two parameters: the qubit energy $\mathrm{\ensuremath{\Omega}}$ and the rate of spontaneous emission $\mathrm{\ensuremath{\Gamma}}$.
We present a time-dependent quantum calculations of the first order and second order photon correlation functions for the scattering of a single-photon pulse on a two-level atom (qubit) embedded in a one-dimensional open waveguide. Within Markov approximation we find the analytic expression for the quantum operator of positive frequency electric field. We restricted Hilbert space of initial states by the states with one and two excitations and show that the photon probability amplitudes are given by the off-diagonal matrix elements of the electric field operator between these states. For two-excitation initial state where the atom is excited and there exists a single photon in a waveguide we calculate the second order correlation function which describes the measurements by two detectors at two different space-time points. The second order correlation function exhibits the interference term showing that the measurements of two detectors are correlated. This interference is similar to that found in the Hanbury Brown and Twiss correlation experiment with two indistinguishable photons.
For a system of two spatially separated qubits (two-level atoms) coupled to a one-dimensional waveguide we have described the time evolution of singly or doubly excited states of the atomic subsystem. When the interatomic distance lll takes special (``resonant'' or ``antiresonant'') values, the singly excited system of resonant atoms can form metastable (dark) states. If lll slightly deviates from one of the special values or the atomic frequencies do not coincide, the dark states slowly decay and we have calculated the decay rate. Also, we have found that the doubly excited state of two resonant atoms located at the special positions does not completely decay but, with a finite probability, can evolve (with the emission of a single photon) to one of the metastable singly excited states. Metastable states of pairs of qubits may find applications (e.g., as memory elements) in information processing or as detectors sensitive to external perturbations.
We present a method for quantum state tomography within a single-excitation subspace of two-qubit states in an open waveguide. The system under investigation consists of three qubits in an open waveguide, separated by a distance comparable to the wavelength of the electromagnetic field. We show that the modulation of the frequency of the central ancillary qubit allows us to obtain unambiguous information about the initial phase difference ${\ensuremath{\varphi}}_{1}\ensuremath{-}{\ensuremath{\varphi}}_{3}$ of the edge qubits via the measurement of the evolution of their probability amplitudes.
The light-matter interaction effects are especially important in one-dimentional (1D) systems, where there is no spatial spreading of emitted radiation. We study Such metastable states of a singly excited pair of resonant atoms arise when the distance between the atoms takes special values We have calculated their decay rate when the interatomic distance deviates from the special values or when the transition frequencies of the two atoms do not coincide (inhomogeneous detuning). Also, we have found that the doubly excited state of two resonant atoms located at the special positions does not completely decay, but with a finite probability can evolve to one of the metastable singly-excited states. Dark states of pairs of qubits may serve as memory elements or sensitive detectors of external perturbations.
In this paper, the scattering of a single photon in a waveguide–resonator–qubit system is studied. An open waveguide is connected to two resonators, located at an arbitrary distance from each other and containing a single qubit each. The scattering of a single photon makes it possible to describe the behavior of the system completely quantum mechanically. We show the existence of Fano resonance, which is a direct manifestation of the interference between the incident photon and virtual photons associated with transitions between the states of the system. The obtained expressions for the transmission coefficients allowed us to take into account the influence of the incident photon frequency on the resonances and their widths.