Waveguide quantum electrodynamics: Controllable channel from quantum interference

Abstract

We study a waveguide QED system with a rectangular waveguide and a two-level system (TLS) inside, where the transverse modes TMmn define the quantum channels of guided photons. It is discovered that the loss of photons in the TM11 channel into the others can be overcome by replacing it with a certain coherent superposition of TMmn channels, which is named as the controllable channel (CC) as the photons in CC can be perfectly reflected or transmitted by the TLS, and never lost into the other channels. The dark state emerges when the photon is incident from one of the scattering-free channels (SFCs) orthogonal to CC. The underlying physics mechanism is the multi-channel interference associated with Fano resonance.PACS numbers: 42.50. Gy, 42.50.Ct, 03.65.Nk In a fully-quantum network based on single photon carriers to process quantum information, the essential task is to coherently control photon propagation by a local quantum node [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. To this end, a hybrid system consisting of a one-dimensional (1D) waveguide coupled to a two-level system (TLS) is extensively studied for physical implementation of the quantum node acting as a quantum switch [4][5][6][7][8][9][10][11][12] or a single photon transistor [13,14]. With the single mode approximation for a waveguide with infinitesimal cross section, the total reflection of single photons by the TLS was found to be responsible for the dominant functions of quantum devices.However, a realistic waveguide with a finite cross section necessarily possesses transverse modes. Thus, photons guided in the realistic waveguide may be in different quantum channels defined by transverse modes. Each transverse mode has a cut-off frequency for the corresponding guiding mode. To demonstrate multi-channel effects on single-photon scattering, Ref.[21] made an approximation using two modes and a quadratic dispersion relation, and showed that the guided photon cannot be totally reflected due to the loss from one mode to the other. In other words, the quantum device oriented functions we desire can not be well achieved . In order to overcome such multi-channel loss, we will revisit the waveguide QED by considering a realistic hybrid system without any over-approximation.In this letter, we study single-photon scattering by a TLS locally embedded in a waveguide of finite rectangular cross section. In our approach, both the real dispersion relation and multi-channel effects are exactly taken into account. As for the multi-channel induced loss, we find that there exists a unique controllable channel (CC) defined by a particular superposition of the transverse magnetic modes TM mn , in which the guided photons can * Electronic address: cpsun@csrc.ac.cn; URL: http://www.csrc.ac.cn/suncp/ be well controlled by the TLS since the guided photons in the complementary channels orthogonal to CC are completely decoupled from the TLS. Such a scattering free channel (SFC) behaves as the dark state to support the electromagnetically induc...

Scattering of two distinguishable photons by aΞ-type three-level atom in a one-dimensional waveguide

“…Such a one-dimensional configuration has been employed in most previous waveguide QED studies. The problem of waveguides with more than one transverse modes has been discussed recently [11,12], but this is beyond the scope of this paper. For simplicity, we assume ω k = v g k and the speed of light in the waveguide v g = 1.…”

“…The transport properties of single photons controlled by interaction with atoms (or artificial atoms) inside a onedimensional waveguide have been a subject of considerable interest in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In waveguide quantum electrodynamics (QED) systems, atoms can strongly interact with a continuum of field modes compared with those in free space, and the propagation directions of photons can be well monitored.…”

Dynamical theory of single-photon transport in a one-dimensional waveguide coupled to identical and nonidentical emitters

“…The stationary results of the photon transport in a waveguide-QED system, including a single photon or multiple photons interacting with a single emitter or multiple emitters, have been extensively studied based on the Bethe-ansatz approach [18][19][20][21][22][23], Lippmann-Schwinger scattering theory [24,25], input-output theory [26][27][28], Lehmann-Symanzik-Zimmermann reduction approach [29], and the diagrammatic method [30]. In addition, dynamical theories, which allow to study the real time evolution of the emitter excitations and photon pulse, have also been studied [31][32][33][34][35].…”

“…In the previous calculations [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], the effect of the non-waveguide vacuum modes is included by simply adding a phenomenological decay factor in the Hamiltonian. This approximation is valid when the emitter separation is of the order of or larger than the resonant wavelength.…”

Reprint of : Photon correlations generated by inelastic scattering in a one-dimensional waveguide coupled to three-level systems

“…The majority of work on these topics has treated a single quantum system coupled to the waveguide, where the single quantum system is modeled as a two-level system (2LS) or the only slightly more complicated driven 3LS (for very recent work along these lines see, for example, Refs. [38][39][40][41]). Correlation effects in a multi-qubit waveguide have been studied in a number of recent papers using a variety of techniques [42][43][44][45][46][47][48][49][50][51][52][53][54][55].…”