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arXiv:1707.02707 · Scientific Reports

Vacuum induced transparency and photon number resolved Autler-Townes splitting in a three-level system

Jiang-hao Ding, Sainan Huai, Hou Ian, Yu-xi Liu

Published Mar 8, 2018• 6 citations
arXivHTMLPDF

Abstract

We study the absorption spectrum of a probe field by a Λ-type three-level system, which is coupled to a quantized control field through the two upper energy levels. The probe field is applied to the ground and the second excited states. When the quantized control field is in vacuum, we derive a threshold condition to discern vacuum induced transparency (VIT) and vacuum induced Autler-Townes splitting (ATS). We also find that the parameter changing from VIT to vacuum induced ATS is very similar to that from broken PT symmetry to PT symmetry. Moreover, we find the photon number resolved spectrum in the parameter regime of vacuum induced ATS when the mean photon number of the quantized control field is changed from zero (vacuum) to a finite number. However, there is no photon number resolved spectrum in the parameter regime of VIT even that the quantized control field contains the finite number of photons. Finally, we further discuss possible experimental realization.

DOI
10.1038/s41598-018-22666-2

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We study the absorption spectrum of a probe field by a Λ-type three-level system, which is coupled to a quantized control field through the two upper energy levels. The probe field is applied to the ground and the second excited states. When the quantized control field is in vacuum, we derive a threshold condition to discern vacuum induced transparency (VIT) and vacuum induced Autler-Townes splitting (ATS). We also find that the parameter changing from VIT to vacuum induced ATS is very similar to that from broken PT symmetry to PT symmetry. Moreover, we find the photon number resolved spectrum in the parameter regime of vacuum induced ATS when the mean photon number of the quantized control field is changed from zero (vacuum) to a finite number. However, there is no photon number resolved spectrum in the parameter regime of VIT even that the quantized control field contains the finite number of photons. Finally, we further discuss possible experimental realization.
Abstract We use biorthogonal basis consisting of the ‘right’ and ‘left’ eigenvectors of the effective non-Hermitian Hamiltonian of a three-level Λ system driven by a bi-chromatic field, and resolve the probe absorption spectrum into components corresponding to the decaying dressed states of the system. It is observed that the spectrum primarily consists of three components and two of them undergo dramatic changes when the control field Rabi frequency is changed from the low to high field regime. Based on the symmetry properties of a combination of these components, a parameter internal to the dynamics of the system is defined and is used to distinguish between electromagnetically induced transparency (EIT) and Autler–Townes (AT) splitting, and the threshold for transition between them in an objective manner. The formulation is further extended to the resonance fluorescence spectrum on the probe transition in the EIT and AT regimes.
Abstract Discerning electromagnetically induced transparency (EIT) from Autler–Townes splitting (ATS) is a significant issue in quantum optics and has attracted wide attention in various three-level configurations. Here we present a detailed study of EIT and ATS in a five-level atomic system considered to be composed of a four-level Y-type subsystem and a three-level Λ-type subsystem. In our theoretical calculations with standard density matrix formalism and steady-state approximation, we obtain the general analytical expression of the first-order matrix element responsible for the probe-field absorption. In light of the well-known three-level EIT and ATS criteria, we numerically show an intersection of EIT with ATS for the Y-type subsystem. Furthermore, we show that an EIT dip is sandwiched between two ATS dips (i.e., multi-dip mixture of EIT and ATS) in the absorption line for the five-level system, which can be explained by the dressed-state theory and Fano interference.
Summary form only given. If in general the transparency of an initially absorbing medium for a probe field is increased by the presence of a control field on an adjacent transition, two very different processes can be invoked to explain it. One of them is a quantum Fano interference between two paths in the three-level system, which occurs even at low control intensity and gives rise to electromagnetically-induced transparency (EIT), the other one is the appearance of two dressed states in the excited level at higher control intensity, corresponding to the Autler-Townes splitting (ATS). This distinction is particularly critical for instance for the implementation of slow light or optical quantum memories. In a recent paper, P. M. Anisimov, J. P. Dowling and B. C. Sanders proposed a quantitative test to objectively discerning ATS from EIT. We experimentally investigated this test with cold atoms and demonstrated that it is very sensitive to the specific properties of the medium. In this study, we use an ensemble of cold Cesium atoms trapped in a MOT, interacting with light via a Λ-type scheme on the D2 line. Absorption profiles are obtained for various values of the control Rabi frequency Ω between 0.1Γ and 4Γ, where Γ is the natural linewidth.
We experimentally study a vacuum-induced Autler-Townes doublet in a superconducting three-level artificial atom strongly coupled to a coplanar waveguide resonator and simultaneously to a transmission line. The Autler-Townes splitting is observed in the reflection spectrum from the three-level atom in a transition between the ground state and the second excited state when the transition between the two excited states is resonant with a resonator. By applying a driving field to the resonator, we observe a change in the regime of the Autler-Townes splitting from quantum (vacuum-induced) to classical (with many resonator photons). Furthermore, we show that the reflection of propagating microwaves in a transmission line could be controlled by different frequency microwave fields at the single-photon level in a resonator.
The absorption and dispersion of probe light is studied in an unified framework of three-level system, with coherent laser driving and incoherent pumping and relaxation. The electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are studied in details. In the phase diagram of the unified three-level system, there are distinct parameter regimes corresponding to different lineshapes and mechanisms, and the incoherent transition could control the cross-over between EIT and ATS. The incoherent control of the three-level system enables the investigation of various phenomena in quantum optics, and is beneficial for experiments of light-matter interactions.
Electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are two phenomena that can affect the transmission of a probe field in the presence of a stronger field, both yielding transparency in the absorption profile. Being able to discriminate these two similar but distinct phenomena is of vital importance. Here we propose a scheme to describe the EIT and ATS phenomena in a plasmonic system. The proposed system consists of one radiative resonator and one subradiant resonator in metal-insulator-metal waveguide, and the transition is observed from the ATS model to the EIT model through three qualitative regions as the coupling strength decreases. In addition, we apply the method proposed by Anisimov to the induced transparency spectrum in our model, and numerically discerning EIT from ATS based on the Akaike's information criterion in a clear way.