Dressed State Formalism Research Articles

Coherent control of dressing interaction of sequential-doubly-dressed four-wave mixing

Abstract We investigate the coherent control of dressing interaction in four-wave mixing (FWM) in a Y-type four-level atomic system based on the dressed states theory. We study the density matrix equation acted by two dressing fields simultaneously governing FWM signal intensity and the eigenvalues under the dressed state formalism. It is shown that the peak position and intensity of Autler–Townes splitting both originate from the dressing interaction as the detuning of the probe field is scanned. Moreover, it is observed that the interaction could be controlled by the dressing fields. Such flexibly controlled nonlinear signal has potential applications in optical communication and quantum information processing.

Light shift induced modification of electromagnetically induced resonances in atomic vapor

We investigate the effects of a third laser on the electromagnetically induced transparency (EIT) spectrum obtained for the D2 line of 87Rb. The third laser converts a typical bi-chromatic laser-induced Λ type system into a four-level N type system. Our work considers two different configurations of N type system depending on whether the third laser is co-propagating or counter-propagating with respect to the other two. The effects of detuning on the EIT spectrum for both cases of N type systems have been experimentally studied. Our results demonstrate that for the counter-propagating case variation of detuning induces a switch from absorption to transmission. We interpret the experimental observations in terms of modification of light shifts by Doppler averaging within a dressed state formalism. Numerical results obtained using the density matrix formulation, which is in good agreement with the experimental results are also included to substantiate the experimental findings. We also find that in the presence of a magnetic field, due to the formation of certain subsystems that involves Zeeman sublevels, neither absorption nor transmission is observed in the probe transmission spectrum. We define these as the “missing resonance” peaks. We propose methods for recovering these peaks in the probe transmission spectrum.

Discerning the transition from electromagnetically induced transparency to Autler–Townes splitting using the decaying dressed state formalism

We use biorthogonal basis consisting of the ‘right’ and ‘left’ eigenvectors of the effective non-Hermitian Hamiltonian of a three-level 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.

Dressed asymptotic states and QED infrared physics

The dressed state formalisms, which incorporate interactions of soft particles into an asymptotic state, are known as the prescriptions expected to solve the problem of infrared (IR) divergence in the quantum field theory (QFT). A particularly famous example is the dressed state formalism proposed by Kulish and Faddeev in quantum electrodynamics (QED). As pointed out by Hirai and Sugishita, however, this formalism has problems in gauge invariance and the IR divergence. These problems are mainly caused by the existence of ghosts or unphysical photon modes. Therefore, we start by studying the asymptotic states in the Coulomb gauge, which excludes ghosts and/or unphysical photon modes. In this paper, we propose a formalism to construct the asymptotic states directly from the interaction of the theory by setting a sufficiently large time scale $T$. In this dressed state formalism, we define the asymptotic interaction remaining at $|t|>T$ in terms of some fixed order of $1/T$, and we are performing all calculations according to that order. We study the asymptotic states in QED specifically, but we can formally apply the dressed state formalism proposed in this paper to any perturbative QFT. We show that, at least in QED, we can construct divergence-free and unitary $S$-matrix using dressed states proposed in this paper. Furthermore, we discuss the transition rate to show that we can predict experimental results. We also show that the $\mathrm{U}(1)$ gauge symmetry of $S$-matrix leads to the QED large gauge symmetry, and deviation of the expectation values of the vector potential between initial and final spacelike hypersurfaces emerges as a QED memory effect. The dressed state formalism in this paper may give a unified and new insight into IR physics, including asymptotic symmetries, memory effects, and unitarity of the state evolution.

Subleading soft dressings of asymptotic states in QED and perturbative quantum gravity

We construct Faddeev-Kulish states in QED and perturbative quantum gravity to subleading order in the soft momentum expansion and to first order in the coupling constant, using the charge conservation formula of asymptotic symmetries associated with the tree-level subleading soft theorems. We demonstrate that the emission and absorption of soft photons/gravitons in dressed amplitudes vanish. The fact that no additional soft radiation may be added to a dressed amplitude supports the claim that, in the dressed state formalism, the soft and hard sectors of scattering processes are correlated. We also show that the dressed virtual amplitudes are equivalent to the infrared-finite part of the traditional amplitudes constructed using Fock states. Since there is no real soft radiation in the asymptotic Hilbert space, the dressed state formalism gives the same cross sections as the Bloch-Nordsieck method.

Dressed states from gauge invariance

The dressed state formalism enables us to define the infrared finite S-matrix for QED. In the formalism, asymptotic charged states are dressed by clouds of photons. The dressed asymptotic states are originally obtained by solving the dynamics of the asymptotic Hamiltonian in the far past or future region. However, there was an argument that the obtained dressed states are not gauge invariant. We resolve the problem by imposing a correct gauge invariant condition. We show that the dressed states can be obtained just by requiring the gauge invariance of asymptotic states. In other words, Gauss’s law naturally leads to proper asymptotic states for the infrared finite S-matrix. We also discuss the relation between the dressed state formalism and the asymptotic symmetry for QED.

Spectral characteristics of a modified inverted-Y system beyond rotating wave approximation

The spectral properties of a multilevel atomic system interacting with multiple electromagnetic fields, a modified inverted-Y system, have been theoretically investigated. In this study, a numerical matrix propagation method has been employed to study the spectral characteristics beyond the validity regime of the rotating wave approximations. The studied atomic system, comprising of several basic sub-systems, i.e. lambda, ladder, vee, N and inverted-Y, is useful to study the interdependence among these basic sub-systems. The key features of the obtained probe spectra as a function of coupling strength and detuning of the associated electromagnetic fields show inter-conversion, splitting and shifting of the transparency and absorption peaks. The dressed and doubly dressed state formalism have been utilized to explain the numerically obtained results. This study has application in design of novel optical devices capable of multi-channel optical communication along with switching.

Collapse and revival oscillation in Double Jaynes–Cummings model

We develop a systematic method of solving two non-interacting Jaynes-Cummings models by using the dressed state formalism in Hilbert space $\mathcal{H}_{AB}^{(2\otimes2)}$. It is shown that such model, called Double Jaynes-Cummings model (D-JCM), can be exactly solved if we take the initial bare state as the linear superposition of two Bell states. The collapse and revival oscillation, which is the standard trait of typical Jaynes-Cummings model, can be recovered if we make measurement at each local sites. Some consequence of the entanglement-induced dressing is discussed.

Interacting superradiance samples: modified intensities and timescales, and frequency shifts

We consider the interaction between distinct superradiance (SR) systems and use the dressed state formalism to solve the case of two interacting two-atom SR samples at resonance. We show that the ensuing entanglement modifies the transition rates and intensities of radiation, as well as introduces a potentially measurable frequency chirp in the SR cascade, the magnitude of which being a function of the separation between the samples. For the dominant SR cascade we find a significant reduction in the duration and an increase of the intensity of the SR pulse relative to the case of a single two-atom SR sample.

Dressed infrared quantum information

We study information-theoretic aspects of the infrared sector of quantum electrodynamics, using the dressed-state approach pioneered by Chung, Kibble, Faddeev-Kulish and others. In this formalism QED has an IR-finite S-matrix describing the scattering of electrons dressed by coherent states of photons. We show that measurements sensitive only to the outgoing electronic degrees of freedom will experience decoherence in the electron momentum basis due to unobservable photons in the dressing. We make some comments on possible refinements of the dressed-state formalism, and how these considerations relate to the black hole information paradox.

Achieving high-fidelity single-qubit gates in a strongly driven silicon-quantum-dot hybrid qubit

Performing qubit gate operations as quickly as possible can be important to minimize the effects of decoherence. For resonant gates, this requires applying a strong ac drive. However, strong driving can present control challenges by causing leakage to levels that lie outside the qubit subspace. Strong driving can also present theoretical challenges because preferred tools such as the rotating wave approximation can break down, resulting in complex dynamics that are difficult to control. Here we analyze resonant $X$ rotations of a silicon quantum double dot hybrid qubit within a dressed-state formalism, obtaining results beyond the rotating wave approximation. We obtain analytic formulas for the optimum driving frequency and the Rabi frequency, which both are affected by strong driving. While the qubit states exhibit fast oscillations due to counter-rotating terms and leakage, we show that they can be suppressed to the point that gate fidelities above $99.99\%$ are possible, in the absence of decoherence. Hence decoherence mechanisms, rather than strong-driving effects, should represent the limiting factor for resonant-gate fidelities in quantum dot hybrid qubits.

Manipulating nanoscale atom–atom interactions with cavity QED

We theoretically explore the manipulation of interactions between excited and ground-state atoms at nanoscale separations by using cavity quantum electrodynamics (CQED). We develop an adiabatic molecular dressed-state formalism and show that it is possible to generate Fano–Feshbach resonances between ground and long-lived excited-state atoms inside a cavity. The resonances are shown to arise due to nonadiabatic coupling near a pseudo-crossing between the dressed-state potentials. We illustrate our results with a model study using fermionic 171Yb atoms in a two-modal cavity. Our study is important for the manipulation of interatomic interactions at low energy by using a cavity field.

Quantum effects at low-energy atom–molecule interface

Quantum interference effects in inter-conversion between cold atoms and diatomic molecules are analysed. Within the framework of Fano's theory, continuum-bound anisotropic dressed state formalism of atom-molecule quantum dynamics is presented. This formalism is applicable in photo- and magneto-associative strong-coupling regimes. The significance of Fano effect in ultracold atom-molecule transitions is discussed. Quantum effects at low energy atom-molecule interface are important for exploring coherent phenomena in hither-to unexplored parameter regimes.

Phase dependent effect on the resonant absorption spectrum in a Ξ-configuration atom driven by a pair of bichromatic fields

The absorption spectrum of the upper transition in a Ξ-configuration three-level atomic system driven by a pair of bichromatic fields is studied. The spectrum exhibits a multipeaked absorption spectrum with a constant peak separation depending on the detuning of the driving field. We find the resonant absorption is suppressed continuously with the increase of the detuning. As a result, for a sufficiently large detuning, the frequency range between inner sidepeaks form an approximately transparent window of which the width can be controlled through adjusting the field detuning. Additionally, we find that the comb-like absorptive spectrum can be turned into an comb-like emissive spectrum when the modulation of phases of the driving fields is involved. The main results are interpreted in term of the dressed-state formalism.

Deflection of a Λ-type three-level atom by a light field: a mechanical demonstration of the coherent population trapping effect

We consider the deflection of a three-level atom of Λ-type interacting with a light field of two coherent laser beams. We employ the dressed state formalism, which is suitable for large Rabi frequencies and/or large detunings. A full study of the interaction and relaxation processes is performed. We show that a beam of atoms is split into three beams once it crosses the light field. This is a three-state version of the well-known optical Stern–Gerlach effect, which has been theoretically studied and experimentally demonstrated for two-level atoms. Under coherent population trapping conditions, the splitting of the beam becomes twofold. This gives us, in principle, the opportunity of a mechanical demonstration of the coherent population trapping effect.

Phase-dependent electromagnetically induced transparency in a four-level atom system

We present a method to control the electromagnetically induced transparency (EIT) in a four-level system with a coupling field, a weak probe field and two microwave driven fields. By sloving the density matrix equations, the numerious result is obtained. It is shown that the EIT resonance can be split into doublets and the spectral position of EIT window is determined by the relative phase between two microwave fields for fixed intensity of the microwave field. Therefore, the microwave field can be used to open more than one EIT window and by controlling their phase difference we can perform EIT frequency tuning. The structure in the spectrum can be explained using the dressed-state formalism.

Adiabatic and diabatic process of sum frequency conversion

Based on the dressed state formalism, we obtain the adiabatic criterion of the sum frequency conversion. We show that this constraint restricts the energy conversion between the two dressed fields, which are superpositions of the signal field and the sum frequency field. We also show that the evolution of the populations of the dressed fields, which in turn describes the conversion of light photons from the seed frequency to the sum frequency during propagation through the nonlinear crystal. Take the quasiphased matched (QPM) scheme as an example, we calculate the expected bandwidth of the frequency conversion process, and its dependence on the length of the crystal. We demonstrate that the evolutionary patterns of the sum frequency field's energy are similar to the Fresnel diffraction of a light field. We finally show that the expected bandwidth can be also deduced from the evolution of the adiabaticity of the dressed fileds.

Quantum coherence in Λ-three-level system driven by bichromatic coupling field

We present a theoretical study of quantum coherent effects in a Λ-three-level system with a strong bichromatic coupling field and a weak probe field. When one component of the strong bichromatic coupling field is resonant with a corresponding transition and the other is detuning with an integer fraction of the Rabi frequency of the resonant field, the absorption spectrum exhibits a series of symmetrical doublets. While two frequencies of the strong bichromatic coupling field are symmetrically detuned from the transition, the position and the relative intensity of the absorption peak are both affected by the coupling field intensity and detuning. An explanation of the spectrum is given in term of the dressed-state formalism.

Controlling collisional spin relaxation of cold molecules with microwave laser fields

We explore the effects of microwave laser fields on spin-changing transitions in collisions of polar molecules in a $^{2}\ensuremath{\Sigma}$ electronic state with atoms in the presence of a static magnetic field. We use the dressed-state formalism of quantum optics to describe the interaction of the radiation field with the collision complex and perform rigorous scattering calculations to study spin-changing transitions in collisions of CaH molecules with He atoms at temperatures below 1 K. Our calculations demonstrate that collision-induced spin relaxation of $^{2}\ensuremath{\Sigma}$ molecules is enhanced near avoided crossings between different Zeeman levels. We show that the positions of the avoided crossings can be modified by varying the frequency and the intensity of the microwave laser field and discuss the mechanisms of microwave field control of spin-dependent interactions in cold open-shell molecules.

Spectral feature with sub-natural linewidth due to quantum interference in a four-level system

This paper studies the narrow spectral feature appearing in a four-level system coupled by two strong coherent fields and probed by a weak laser field. The linewidth is examined as a function of the Rabi frequencies of coupling fields, and the result is explained by using the dressed-state formalism.