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arXiv:1405.2383 · Physical Review A

Quantum coherence and population transfer in a driven cascade three-level artificial atom

Sung Un Cho, Han Seb Moon, Young-Tak Chough, Myung‐Ho Bae, Nam Kim

Published May 12, 2014• 15 citations
arXivHTMLPDF

Abstract

We present an experimental investigation on the spectral characteristics of an artificial atom ``transmon qubit'' constituting a three-level cascade system ($\ensuremath{\Xi}$-system) in the presence of a pair of external driving fields. We observe two different types of Autler-Townes (AT) splitting: type I, where the phenomenon of two-photon resonance tends to diminish as the coupling field strength increases, and type II, where this phenomenon mostly stays constant. We find that the types are determined by the cooperative effect of the decay rates and the field strengths. Theoretically analyzing the density-matrix elements in the weak-field limit where the AT effect is suppressed, we single out events of pure two-photon coherence occurring owing to constructive quantum interference.

DOI
10.1103/physreva.89.053814

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•Jun 1, 2006•0 citations
We present an experimental investigation on the spectral characteristics of an artificial atom ``transmon qubit'' constituting a three-level cascade system (\ensuremathΞ\ensuremath{\Xi}\ensuremathΞ-system) in the presence of a pair of external driving fields. We observe two different types of Autler-Townes (AT) splitting: type I, where the phenomenon of two-photon resonance tends to diminish as the coupling field strength increases, and type II, where this phenomenon mostly stays constant. We find that the types are determined by the cooperative effect of the decay rates and the field strengths. Theoretically analyzing the density-matrix elements in the weak-field limit where the AT effect is suppressed, we single out events of pure two-photon coherence occurring owing to constructive quantum interference.
We present a theoretical study of multiwave mixing in a driven superconducting quantum qubit (artificial atom) with a cyclic Ξ-type three-level structure. We first show that three-wave mixing (3WM), four-wave mixing (4WM), and five-wave mixing (5WM) processes can coexist in the microwave regime in such an artificial system due to the absence of selection rules. Because of electromagnetically induced transparency suppression of linear absorption in a standard Ξ-type configuration, the generated 4WM is enhanced greatly and its efficiency can be as high as 0.1% for only a single artificial atom. We also show that Autler-Townes splitting occurs in the 3WM and 5WM spectra and quantum interference has a significant impact on the total signal intensity being a coherent superposition of these two signals.
We derive the statistics of scattered photons from a $\ensuremath{\Lambda}$- or ladder-type three-level emitter (3LE) embedded in a one-dimensional open waveguide. The weak probe photons in the waveguide are coupled to one of the two allowed transitions of the 3LE, and the other transition is driven by a control beam. This system shows electromagnetically induced transparency, which is accompanied with the Autler-Townes splitting (ATS) at a strong driving by the control beam, and some of these effects have been observed recently. We show that the nature of second-order coherence of the transmitted probe photons near two-photon resonance changes from bunching to antibunching to constant as the strength of the control beam is ramped up from zero to a higher value where the ATS appears.
We investigate quantum interference and classical-interference effects when three-level atoms in the ``$\ensuremath{\Lambda}$'' or ``V'' configuration interact with both a cavity-field mode and an external driving field mode. We describe electromagnetically induced transparency ($\ensuremath{\Lambda}$ configuration), as well as a ``field-induced transparency'' (V configuration), and we go beyond the weak cavity-field studies of previous papers by utilizing a Heisenberg-picture density matrix approach. We find that under certain circumstances the cavity field evolves to be equal in magnitude to, but $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase with, the external pump field when the pump-field frequency equals the cavity frequency, a surprising effect found in two-level atoms in a cavity excited by an external pump field that persists in three-level atoms. The better the cavity, the quicker this buildup occurs. When the cavity field reaches this ``out-of-phase'' condition, the resonance fluorescence from the atom in the cavity goes to zero. This is a purely classical-interference effect between the two out-of-phase fields, with the resonance fluorescence going to zero at the same time as the two excited state populations go to zero. This is quite different from the quantum interference that occurs under the right circumstances when the state populations are coherently driven into a linear combination that is decoupled from any applied field and population is trapped in the excited states (``coherent population trapping''). When the cavity frequency is tuned to the frequency at which quantum interference would occur, the two interference effects compete with each other. The cavity field begins to evolve toward the $180\ifmmode^\circ\else\textdegree\fi{}$ out-of-phase condition, thereby approaching a classical destructive interference condition with the pump field. Then at some point before 100% classical interference occurs, depending on the cavity damping rate and atom/cavity coupling strength, the atom builds up its coherence between state populations to produce the quantum interference effect. At that point, the atom becomes transparent and resonance fluorescence disappears, including fluorescence into the cavity, thereby causing the cavity field to die away.
Based on a calculation model, we study the interference phenomena of serially coupled V-type and Λ-type triple quantum dots (CTQDs) driven simultaneously by a strong driving field and a weak probe field. Strongly depending on the configuration of the three-level CTQD, the probe absorption spectra, which are shown in the tunneling current, exhibit various quantum coherence properties. In the case where the two pairs of transitions of the CTQD have a small eigenfrequency difference Δω, the double-coupling effect of the driving field results in two Autler—Townes doublets and one weak Mollow triplet in one spectrum. With the value of Δω increasing, only one Autler—Townes splitting remains due to the single-coupling of the field. We also find that the effect of spontaneous emission of phonons may lead to an obvious background current, which can be used to distinguish which transition is driven by the driving field in experiment. The interesting quantum property of a CTQD revealed in our results suggests its potential applications in quantum modulators and quantum logic devices.
We study the quantum interference in two-photon resonant nondegenerate four-wave mixing (NFWM) in a dressed cascade four-level system in which the two upper levels are coupled by a strong laser field. We find that in the presence of a strong coupling field, two-photon resonant NFWM spectrum exhibits Autler-Townes splitting, which reflects the levels of the dressed states. It also leads to either suppression or enhancement of the NFWM signal. This scheme involves the resonant three-photon excitation, therefore, provides a new spectroscopic tool for studying highly excited atomic states with high sensitivity.
The appearance of quantum interference in the microscopic world is one of the deepest mysteries at the very root of quantum mechanics. When light interacts with atoms, it can induce transitions by way of distinct but indistinguishable pathways and yield unexpected and often counter-intuitive results. Electromagnetically Induced Transparency (EIT), Coherent Population Trapping (CPT), and Lasing Without Inversion (LWI) are modern examples of phenomena where the traditional rules that govern absorption and dispersion undergo major revisions. Spectacular consequences of this new state of affairs include the ability of a light beam to propagate through a normally absorbing medium with little or no absorption, or to undergo amplification even if the active medium is not prepared in a state of population inversion. Light signals have been shown to travel with strongly subluminal group velocities of only a handful of meters per second and, even, to propagate at speed greater than the ordinary speed of light, but without violation of causality or of the established rules that control the transfer of optical information through space. Three-level atoms can interact with two coherent electromagnetic fields according to three different systems, known as Cascade, Lambda and Vee systems. The propagation of a weak probe field can be deeply affected by the presence of a second stronger beam, the so-called coupling field. Transparency windows, splitting of emission and absorption lines and enormously enhanced dispersion have been documented in numerous experiments. In this thesis we explore the physical origin of the transparency induced in these systems by the simultaneous interplay of the coupling and probe fields. We focus our attention on the Cascade system and study its two configurations, Cascade-EIT and Cascade-AT. We develop a variety of complementary approaches for the description of these two configurations, some semiclassical and others fully quantum mechanical. We prove the existence of quantum interference in Electromagnetically Induced Transparency and also the surprising absence of interference in a closely related phenomenon, known as the Autler-Townes effect. Finally we complement the traditional machinery of theoretical quantum optics with techniques borrowed from quantum scattering theory, and offer what we believe is the most convincing physical evidence for the appearance, or for the absence, of quantum interference effects.