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arXiv:1608.05523 · Physical Review A

Mollow triplet through pump-probe single-photon spectroscopy of artificial atoms

Ya. S. Greenberg, A. N. Sultanov

Published May 12, 2017• 5 citations
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Abstract

We analyze a photon transport through a one-dimensional open waveguide side coupled to the $N$-photon microwave cavity with embedded an 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 a non-Hermitian Hamiltonian approach we develop a one-photon approximation scheme to obtain the photon wave function, which allows for the calculation of the probability amplitudes of the spontaneous transitions between the levels of two Rabi doublets in an $N$-photon cavity. We obtain analytic expressions for the transmission and reflection factors of the microwave signal through a waveguide which contains the information of the qubit parameters. We show that for a small number of cavity photons the Mollow spectrum consists of four spectral lines, which is a direct manifestation of the quantum nature of light. The results obtained in the paper are of a 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 $\mathrm{\ensuremath{\Omega}}$ of the qubit and its coupling $\ensuremath{\lambda}$ to the cavity photons.

DOI
10.1103/physreva.95.053840

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We analyze a photon transport through a one-dimensional open waveguide side coupled to the NNN-photon microwave cavity with embedded an 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 a non-Hermitian Hamiltonian approach we develop a one-photon approximation scheme to obtain the photon wave function, which allows for the calculation of the probability amplitudes of the spontaneous transitions between the levels of two Rabi doublets in an NNN-photon cavity. We obtain analytic expressions for the transmission and reflection factors of the microwave signal through a waveguide which contains the information of the qubit parameters. We show that for a small number of cavity photons the Mollow spectrum consists of four spectral lines, which is a direct manifestation of the quantum nature of light. The results obtained in the paper are of a 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 \ensuremathΩ\mathrm{\ensuremath{\Omega}}\ensuremathΩ of the qubit and its coupling \ensuremathλ\ensuremath{\lambda}\ensuremathλ to the cavity photons.
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 $\mathrm{\ensuremath{\Gamma}}$.
In this work, using the non-Hermitian Hamiltonian method, the transmission of a single photon in a one-dimensional waveguide interacting with the cavity containing an arbitrary number of photons and the two-level artificial atom is studied with allowance for the relaxation of the latter. For transport factors, analytical expressions which explicitly take into account the qubit relaxation parameter have been obtained. The form of the transmission (reflection) coefficient when there is more than one photon in the cavity qualitatively differs from the single-photon cavity and contains the manifestation of the photon blockade effect. The qubit lifetime depends on the number of photons in the cavity.
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.
We study the transmission and reflection properties of a single-photon pulse in a one-dimensional waveguide side coupled with a Jaynes-Cummings system, namely, a multi-cavity with an embedded Rydberg atom. A Single-photon pulse is applied to tune the atoms energy spectrum, and varying it can bring the atomic qubit transition on or off-resonance for the cavity. The transmission and reflection behavior are systematically explored by a real-space model Hamiltonian and we find that the coupling strength between the waveguide and the side optical cavity exerts a tremendous impact on it. The influence of cavity and atomic dissipations and the incident pulse width on the transport properties of the single-photon is also investigated simultaneously. Based on these phenomena, we point out the possibility of utilizing this system as a single-photon transport in practice and has potential applications in quantum information.
We experimentally demonstrate the resonance fluorescence of a two-level artificial atom strongly coupled to a single-mode cavity field. The effect was theoretically predicted thirty years ago by Savage [Phys. Rev. Lett. 63, 1376 (1989)]. The system consists of a superconducting qubit circuit and a one-dimensional transmission line resonator. In addition, a one-dimensional transmission line strongly coupled to the atom serves as an open space. The effect takes place, when a microwave field is applied to the cavity, which in turn is resonantly coupled to the atom. The fluorescence spectrum is measured via the emission into the transmission line. We find that the central peak is determined by the atom spontaneous emission to the open space and the widths of side peaks are largely determined by the coherent interaction between the atom and the cavity, that is, the fluorescence spectrum here is very different from that of the Mollow triplet. We also derive analytical form for the spectrum. Our experimental results agree well with theoretical calculations.
We address recent advances in microwave quantum optics with artificial atoms in one-dimensional (1D) open space. This field relies on the fact that the coupling between a superconducting artificial atom and propagating microwave photons in a 1D open transmission line can be made strong enough to observe quantum coherent effects, without using any cavity to confine the microwave photons. We investigate the scattering properties in such a system with resonant coherent microwaves. We observe the strong nonlinearity of the artificial atom and under strong driving we observe the Mollow triplet. By applying two resonant tones, we also observe the Autler–Townes splitting. Exploiting these effects, we demonstrate two quantum devices at the single-photon level in the microwave regime: the single-photon router and the photon-number filter. These devices provide important steps toward the realization of an on-chip quantum network.