arXiv subjects

Ya. S. Greenberg

Publications and source records attributed to Ya. S. Greenberg.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Rabi oscillations of a qubit strongly coupled to a one-dimensional waveguide

We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.

quant-ph↗

arXiv2026

Decay of transmon qubit in a broadband one-dimensional cavity

We investigate the decay dynamics of a three-level artificial atom, a superconducting transmon qubit, weakly coupled to a continuum of modes in a broadband, one-dimensional cavity. Using the resolvent formalism, we derive analytical expressions for the resonance frequency shifts and widths, which are then evaluated numerically for a Gaussian density of states. We identify two distinct dynamical regimes, differentiated by the ratio of the qubit's coupling strength to the continuum bandwidth. When this ratio is much less than one, the system exhibits a Markovian regime in which the resonance width is practically independent of energy within the continuum band. As the ratio increases, the system transitions to a non-Markovian regime where the resonance width becomes strongly energy-dependent. In this regime, the qubit interacts with the continuum faster than the continuum can erase the information from the qubit's past. Furthermore, we demonstrate that the coupling between the transmon's second level and its ground state significantly influences the decay dynamics of the third level. The interaction between these two levels opens a fast two-photon decay channel, which broadens the transmon's second level.

quant-ph↗

arXiv2026

Spontaneous emission of a three-level artificial atom in a one-dimensional open waveguide

We study the dynamical and spectral characteristics of a quantum three-level ladder system, interacting with a continuous electromagnetic field in one-dimensional open waveguide. Common realization of such systems is a waveguide QED setup - a superconducting artificial atom (transmon), coupled to an open microwave transmission line. We derive an analytical solution for spontaneous emission of initially excited atom, and use it to study the probability of state detection and spectral density of output photon states. We find that for strong coupling of transmon to a waveguide emitted photons show correlation in frequency and can have the same energies, even if the three-level system is anharmonic.

quant-ph↗

arXiv2024

Dynamical theory of single-photon transport through a qubit chain coupled to a one-dimensional nanophotonic waveguide

We study the dynamics of a single-photon pulse travelling through a linear qubit chain coupled to continuum modes in a one-dimensional (1D) photonic waveguide. We derive a time-dependent dynamical theory for qubit amplitudes and for transmitted and reflected spectra. We show that the requirement for the photon-qubit coupling to exist only for positive frequencies can significantly change the dynamics of the system. First, it leads to an additional photon-mediated dipole-dipole interaction between qubits which results in the violation of the phase coherence between them. Second, the spectral lines of transmitted and reflected spectra crucially depend on the shape of the incident pulse and the initial distance between the pulse center and the first qubit in the chain. We apply our theory to one-qubit and two-qubit systems. For these two cases, we obtain the explicit expressions for the qubits' amplitudes and the photon radiation spectra as time tends to infinity. For the incident Gaussian wave packet we calculate the line shapes of transmitted and reflected photons.

quant-ph↗

arXiv2023

Single-photon scattering on a two-qubit system. Spatio-temporal structure of the scattered field

In this paper, we study the spatiotemporal distribution of the photon electric field produced by the scattering of a single photon narrow pulse from a system of two identical qubits coupled to continuum modes in a one-dimensional (1D) open waveguide. We derive the time-dependent dynamical equations for qubits' and photon amplitudes which allow the calculation of the photon backward and forward scattering fields in the whole space: before qubits, between qubits, and behind the qubits. The scattered field consists of several contributions that describe a free field of incoming photon, a spontaneous exponential decay of excited qubits, a slowly decaying part that dies out as the inverse powers of $t$, and a lossless part that represents a steady state solution as $t\rightarrow\infty$. For our system, we find the transmittance and reflectance fields as both time and distance from the qubits tend to infinity. We show that as the time after the event of scattering tends to infinity, the steady state photon the field is being formed in the whole one-dimensional space. If the distance $d$ between qubits is equal to the integer of the wavelength $λ$, the field energy exhibits temporal beatings between the qubit frequency $Ω$ and the photon frequency $ω_S$ with the period $T=2π/(ω_S-Ω)$.

quant-ph↗

arXiv2022

Single-photon scattering on a qubit. Space-time structure of the scattered field

We study the space-time structure of the scattered field induced by the scattering of a narrow single-photon Gaussian pulse on a qubit embedded in 1D open waveguide. For a weak excitation power we obtain explicit analytical expressions for space and time dependence of reflected and transmitted fields which are, in general, are different from plain travelling waves. The scattered field consists of two parts: a damping part which represent a spontaneous decay of the excited qubit and a coherent, lossless part. We show that for large distance $x$ from qubit and at times $t$ long after the scattering event our theory provides the result which is well known from the stationary photon transport. However, the approach to the stationary limit is very slow. The scattered field decreases as the inverse powers of $x$ and $t$ as both the distance from the qubit and the time after the interaction increase.

quant-ph↗

arXiv2022

Quantum phase measurement for two-qubit states in an open waveguide

We present a new 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 $φ_1-φ_3$ of the edge qubits via the measurement of the evolution of their probability amplitudes.

quant-ph↗

arXiv2022

Superradiant emission spectra of a two-qubit system in circuit quantum electrodynamics

In this paper we study the spontaneous emission spectra and the emission decay rates of a simplest atom system that exhibits sub- and superradiant properties: a system which consists of two artificial atoms (superconducting qubits) embedded in a one-dimensional open waveguide. The calculations are based on the method of the transition operator which was firstly introduced by R. H. Lehmberg to theoretically describe the spontaneous emission of two-level atoms in a free space. We obtain the explicit expressions for the photon radiation spectra and the emission decay rates for different initial two-qubit configurations with one and two excitations. For every initial state we calculate the radiation spectra and the emission decay rates for different effective distances between qubits. In every case, a decay rate is compared with a single qubit decay to show the superradiant or subradiant nature of a two-qubit decay with a given initial state.

quant-ph↗

arXiv2022

Transition operator approach for the description of spontaneous decay in a multi-qubit system

In this paper we discuss the use of the transition operator method for the theoretical description of a multi-qubit system in a one-dimensional waveguide. A general calculation has been performed for the N-qubit system, which was then applied to the case of spontaneous decay for one and two qubits. The probabilities of transitions in such systems, as well as the emission spectra, are investigated in detail.

quant-ph↗

arXiv2021

Spontaneous decay of artificial atoms in a three-qubit system

We study the evolution of qubits amplitudes in a one-dimensional chain consisting of three equidistantly spaced noninteracting qubits embedded in an open waveguide. The study is performed in the frame of single-excitation subspace, where the only qubit in the chain is initially excited. We show that the dynamics of qubits amplitudes crucially depend on the value of $kd$, where $k$ is the wave vector, $d$ is a distance between neighbor qubits. If $kd$ is equal to an integer multiple of $π$, then the qubits are excited to a stationary level. In this case, it is the dark states which prevent qubits from decaying to zero even though they do not contribute to the output spectrum of photon emission. For other values of $kd$ the excitations of qubits exhibit the damping oscillations which represent the vacuum Rabi oscillations in a three-qubit system. In this case, the output spectrum of photon radiation is determined by a subradiant state which has the lowest decay rate. We also investigated the case with the frequency of a central qubit being different from that of the edge qubits. In this case, the qibits decay rates can be controlled by the frequency detuning between the central and the edge qubits.

quant-ph↗

arXiv2021

Spontaneous decay of artificial atoms in a multi-qubit system

We consider a one-dimensional chain of N equidistantly spaced noninteracting qubits embedded in an open waveguide. In the frame of single-excitation subspace, we systematically study the evolution of qubits amplitudes if the only qubit in the chain was initially excited. We show that the temporal dynamics of qubits amplitudes crucially depend on the value of kd, where k is the wave vector, d is a distance between neighbor qubits. If kd is equal to an integer multiple of $π$, then the qubits are excited to a stationary level which scales as SN^{-1}S. We show that in this case, it is the dark states which prevent qubits from decaying to zero even though they do not contribute to the output spectrum of photon emission. For other values of kd the excitations of qubits have the form of damping oscillations, which represent the vacuum Rabi oscillations in a multi-qubit system. In this case, the output spectrum of photon radiation is defined by a subradiant state with the smallest width.

quant-ph↗

arXiv2020

Waveguide bandgap N-qubit array with a tunable transparency resonance

We study a single photon transmission through 1D N- qubit chain. The qubits are supposed to be identical with equal distance between neighbors. We express the transfer matrix of N- qubit chain in terms of Chebyshev polynomials, which allows us to obtain simple expressions for the transmission and reflection amplitudes for arbitrarily large N. If the distance between neighbor qubits is equal to half wavelength, the transmission spectrum exhibits a flat bandgap structure with very steep walls. We show that for odd N the tuning of the excitation frequency of a central qubit gives rise to the appearance within a bandgap of a narrow resonance with a full transmission. The position of the resonance and its width can be controlled by the frequency of a central qubit. We show that the formation of the bandgap and of the transmission resonance is conditioned by the overlapping the widths of individual qubits which results from the strong coupling between qubits and waveguide photons.

cond-mat.mes-hall↗

arXiv2020

Excitation of the collective states in a three-qubit system

In the present paper, we have proposed the experimentally achievable method for the characterization of the collective states of qubits in a linear chain. We study temporal dynamics of absorption of a single-photon pulse by three interacting qubits embedded in a one-dimensional waveguide. Numerical simulations were performed for a Gaussian-shaped pulse with different frequency detunings and interaction parameters between qubits. The dynamic behavior of the excitation probability for each qubit is investigated. It was shown that the maximum probability amplitudes of excitation of qubits are reached when the frequency of external excitation coincides with the frequency of excitation of the a corresponding eigenstate of the system. In this case, the the magnitude of the probability amplitude of each qubit in the chain unambiguously correlates with the contribution of this qubit to the corresponding collective state of the system, and the decay of these amplitudes are determined by the resonance width arising from the interaction of the qubit with the photon field of the waveguide. Therefore, we show that the pulsed harmonic probe can be used for the characterization of the energies, widths, and the wavefunctions of the collective states in a one-dimensional qubit chain.

cond-mat.mes-hall↗

arXiv2018

Universal tool for single-photon circuits: quantum router design

We demonstrate that the non-Hermitian Hamiltonian approach can be used as a universal tool to design and describe a performance of single photon quantum electrodynamical circuits(cQED). As an example of the validity of this method, we calculate a novel six port quantum router, constructed from 4 qubits and 3 open waveguides. We have got analytical expressions, which describe the transmission and reflection coefficients of a single photon in general form taking into account the non-uniform qubit's parameters. We show that, due to naturally derived interferences, it is possible to tune the probability of photon detection in different ports in-situ.

cond-mat.mes-hall↗

arXiv2018

Influence of Impurity on the Rate of Single Photon Superradiance in Disordered N Qubit Chain

We investigate the rate of superradiant emission for a number of artificial atoms (qubits) embedded in a one-dimensional open waveguide. More specifically, we study the 1D (N+1)- qubit chain where N qubits are identical in respect to their excitation frequency $Ω$ but have different rates of spontaneous emission $Γ_n$, and a single impurity qubit which is different from N qubits by its excitation frequency $Ω_P$ and rate of spontaneous emission $Γ_P$. This system is shown to have two hybridized collective states which accumulates the widths of all qubits. The energy spectrum of these states and corresponding probabilities are investigated as the function of the frequency detuning between the impurity and other qubits in a chain. It is shown that the inclusion of impurity qubit alter the resonance widths of the system only in a narrow range of the frequency detuning between qubits and impurity, where the resonance widths experience a significant repulsion. The photon transmission through disordered N- qubit chain with impurity qubit is also considered. It is shown that a single photon transport through this system is described by a simple expression which predicts for specific photon frequency the existence of a complete transmission peak and transparency window between frequencies $Ω$ and $Ω_P$.

cond-mat.mes-hall↗

arXiv2017

Influence of qubits' nonradiative decay into a common bath on the transport properties of microwave photons

We consider the influence of nonradiative damping of qubits on the microwave transport of photons, propagating in an open one-dimensional microstrip line. Within the framework of the formalism of a non-Hermitian Hamiltonian we obtained the expressions for the transmission and reflection coefficients for two qubits which explicitly account for the indirect interaction between qubits due to nonradiative decay into common bath. It is shown that this interaction leads to the results that are significantly different from those already known

cond-mat.mes-hall↗

arXiv2017

Single photon superradiant decay of cyclotron resonance in a p-type single-crystal semiconductor film with a cubic structure

We study a single-photon super-radiance under the conditions of cyclotron resonance in a perfect single-crystal p-type semiconductor film with cubic structure. We show that the rate of super-radiant emission scales with tjhe film area. which allows one to specify the size of the film at which the probability of a single-photon super-radiance becomes much greater than the probabilities of other scattering channels. The power of super-radiant emission depends only on three fundamental constants: the electron charge q_{e}, the speed of light c, the electron mass m_{e}, and on the electric- to magnetic field ratio.

cond-mat.str-el↗

arXiv2017

Mollow triplet: pump probe single photon spectroscopy of artificial atoms

We analyze a photon transport through an 1D open waveguide side coupled to the $N$-photon microwave cavity with embedded artificial two- level atom (qubit). The qubit state is probed by a weak signal at the fundamental frequency of the waveguide. Within the formalism of projection operators and non-Hermitian Hamiltonian approach we develop a one-photon approximation scheme to obtain the photon wavefunction which allows for the calculation of the probability amplitudes of the spontaneous transitions between the levels of two Rabi doublets in $N$- photon cavity. We obtain analytic expressions for the transmission and reflection factors of the microwave signal through a waveguide, which contain the information of the qubit parameters. We show that for small number of cavity photons the Mollow spectrum consists of four spectral lines which is a direct manifestation of quantum nature of light. 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 energy $Ω$ of the qubit and its coupling $λ$ to the cavity photons.

cond-mat.mes-hall↗