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arXiv:2203.01401 · Physical Review Research

Optical precursors in waveguide quantum electrodynamics

Silvia Cardenas-Lopez, Pablo Solano, Luis A. Orozco, Ana Asenjo-Garcı́a

Published Feb 22, 2023• 4 citations
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Abstract

When a broadband signal propagates through a dispersive medium, some frequency components move faster than the center of the pulse. This leads to the appearance of precursors, transient signals that emerge from the medium earlier than the main part of the pulse and seem to propagate superluminally. Here, we investigate the microscopic origin of precursors in a minimal setup: an array of qubits coupled to a waveguide. The linear transmission function only converges to that of a continuous medium for large qubit numbers. Nevertheless, the dispersion produced by only two qubits is enough to produce oscillatory transients. Precursors are best observed under conditions of electromagnetically induced transparency, as the center of the pulse is significantly delayed. Under these conditions, just a single qutrit is enough to generate a precursor. Our results pave the way towards dispersion engineering of light with just a few qubits and can be realized with superconducting qubits coupled to transmission lines or atoms coupled to optical waveguides.

DOI
10.1103/physrevresearch.5.013133

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When a broadband signal propagates through a dispersive medium, some frequency components move faster than the center of the pulse. This leads to the appearance of precursors, transient signals that emerge from the medium earlier than the main part of the pulse and seem to propagate superluminally. Here, we investigate the microscopic origin of precursors in a minimal setup: an array of qubits coupled to a waveguide. The linear transmission function only converges to that of a continuous medium for large qubit numbers. Nevertheless, the dispersion produced by only two qubits is enough to produce oscillatory transients. Precursors are best observed under conditions of electromagnetically induced transparency, as the center of the pulse is significantly delayed. Under these conditions, just a single qutrit is enough to generate a precursor. Our results pave the way towards dispersion engineering of light with just a few qubits and can be realized with superconducting qubits coupled to transmission lines or atoms coupled to optical waveguides.
Optical precursors were first studied by Sommerfield and Brillouin in 1914 to resolve the apparent contradictions between fast light propagation and the theory of relativity. They showed theoretically that the front edge of a step-modulated pulse does not interact with the medium and always travels at c because the dispersive material has a finite response time to the optical pulse. The past experimental studies of precursors in classical pulse propagation were always focused on an opaque medium with single or multiple Lorentz absorption lines. In these cases, the precursor signal cannot be separated from the main pulse or otherwise the main field is absorbed. However, the electromagnetically induced transparency (EIT) technique was successfully used to separate precursors from the main pulse due to the slow-light effect in cold atoms. The EIT refers to the absorption suppression or elimination of a probe field through atomic coherence in a certain medium dressed by a strong coupling field. In this paper, a four-level double-lambda atomic system with two upper states coupled to the excited state is explored to separate optical precursors from a square-modulated laser pulse with the effect of spontaneously generated coherence (SGC). The SGC effect occurs in the process of spontaneous emission, in which the atom decays from closely placed upper levels to a single ground level. The quantum interference between the decay channels takes place, which leads to decay induced transparency, thus enhancing the Kerr nonlinearity and amplification without inversion. With the assistance of spontaneously generated coherence, an EIT window appears with steep normal dispersion when the trigger field is far from resonance. Then we can obtain the optical precursors which are separated from the main pulse due to the slow-light effects in the EIT window. In the absence of SGC, the main pulse is absorbed by an opaque medium with Lorentz absorptive lines, so the slow-light effect could not take place. In addition, we obtain the stacked optical precursors with the input probe field amplitude or phase modulated by designing a series of square pulses. For the amplitude modulation case, the peak power reaches about 4.5 times that of the input pulse. With the phase modulation we obtain a transient pulse with a peak power of 14 times that of the input, as a result of constructive interference between the stacked precursors and main field. We expect these findings to be instructive in devising optical devices for optical communication, detection and medical imaging among other applications.
We theoretically demonstrated the possible emergence of slow-light self-induced transparency solitons in the infinite one-dimensional coupled cavity array, with each cavity containing a single qubit. We have predicted a substantial dependence of pulse transparency on its dimensionless width τ0τ_0τ0​. In particular, short pulses whose widths range from τ0≪1τ_0\ll 1τ0​≪1 to τ0≲1τ_0\lesssim 1τ0​≲1 exhibit simple, almost linear dispersion law with a finite frequency gap of the order of the cavity array photonic band gap. That is, the medium is opaque for very short pulses with carrier wave frequency below the photonic gap. When the pulse width exceeds the critical one, a twin transparency window separated by a finite band gap appears in the soliton pulse dispersion law. Observation of predicted effects within the proposed setup would be of interest for understanding the properties of self-induced transparency effect in general and future applications in the design of quantum technological devices.
We experimentally examined the propagation of temporally square modulated optical pulses through a coupled ring resonator. Sharp transient spikes appeared as the square pulses entered the system. The main signal gradually grew up through coupled-resonator-induced transparency (CRIT), with the time constant determined by a second resonator. Transient spikes were attributed to the higher and lower spectral components of the incident pulse, to which the resonators cannot respond; hence, they were interpreted as optical precursors. The experiments, therefore, demonstrated that precursors and the main signal can be observed separately, with amplitudes comparable to that of the incident step in CRIT.
We study single-photon-induced electromagnetically induced transparency (EIT) in many-emitter waveguide quantum electrodynamics (wQED) with linear, nonlinear, and quasilinear waveguide dispersion relations. In the single-emitter problem, in addition to the robustness of the EIT spectral features in the overcoupled regime of wQED, we find that the nonlinear dispersion results in the appearance of a side peak for frequencies smaller than the resonant EIT frequency, which turns into a plateau as the nonlinearity is reduced. The quasilinear case produces a similar spectrum to the purely linear scenario with a small observable difference in the far-detuned regime. Consequently, for many-emitter scenarios, our results indicate the formation of band structure for purely linear cases, which, for smaller values of nonlinearity, leads to a narrow band-gap-like structure compared to the corresponding linear and quasilinear dispersion cases. Long-distance quantum networking aided with quantum memories can serve as one of the targeted applications of this work.