Superposition Of Coherent States Research Articles

One point functions for black hole microstates

We compute one point functions of chiral primary operators in the D1–D5 orbifold CFT, in classes of states corresponding to microstates of two and three charge black holes. Black hole microstates describable by supergravity solutions correspond to coherent superpositions of states in the orbifold theory and we develop methods for approximating one point functions in such superpositions in the large N limit. We show that microstates built from long strings (large twist operators) have one point functions that are suppressed by powers of N. Accordingly, even when these microstates admit supergravity descriptions, the characteristic scales in these solutions are comparable to higher derivative corrections to supergravity.

Observation of Interference between Resonant and Detuned stirap in the Adiabatic Creation of ^{23}Na^{40}K Molecules.

Stimulated Raman adiabatic passage (stirap) allows efficiently transferring the populations between two discrete quantum states and has been used to prepare molecules in their rovibrational ground state. In realistic molecules, a well-resolved intermediate state is usually selected to implement the resonant stirap. Because of the complex molecular level structures, the detuned stirap always coexists with the resonant stirap and may cause unexpected interference phenomenon. However, it is generally accepted that the detuned stirap can be neglected if compared with the resonant stirap. Here we report on the first observation of interference between the resonant and detuned stirap in the adiabatic creation of ^{23}Na^{40}K ground-state molecules. The interference is identified by observing that the number of Feshbach molecules after a round-trip stirap oscillates as a function of the hold time, with a visibility of about 90%. This occurs even if the intermediate excited states are well resolved, and the single-photon detuning of the detuned stirap is about 1 order of magnitude larger than the linewidth of the excited state and the Rabi frequencies of the stirap lasers. Moreover, the observed interference indicates that if more than one hyperfine level of the ground state is populated, the stirap prepares a coherent superposition state among them, but not an incoherent mixed state. Further, the purity of the hyperfine levels of the created ground state can be quantitatively determined by the visibility of the oscillation.

Quantum coherences reveal excited-state dynamics in biophysical systems

Ultrafast, multi-dimensional spectroscopic measurements of photosynthetic light-harvesting complexes have revealed quantum coherences with timescales comparable to those of energy-transfer processes. These observations have led to a debate regarding the states that give rise to the coherences and whether the presence of the coherences has implications for photosynthetic light harvesting. In these experiments, laser pulses create a coherent superposition of quantum states with a defined phase relationship across an ensemble, which gives rise to the quantum coherence and associated quantum beating signal. Dephasing of these quantum coherences, seen as a decay of the beating signal, is among the most sensitive probes of the interactions between a system and its surrounding environment. In this Review, we discuss the proposed origin and assignment of the observed quantum coherences in photosynthetic systems as electronic, vibronic or vibrational. We describe the latest experimental efforts towards unravelling the nature of the coherences, in particular ultrafast, two-dimensional electronic spectroscopy, as well as the accompanying theoretical and computational results. We discuss how measuring coherences can inform us about the excited-state dynamics of biophysical and chemical systems relevant to natural light harvesting and how these measurements reveal electronic structure beyond that captured by simplistic models. Femtosecond spectroscopy of photosynthetic systems reveals long-lived quantum coherences. This Review focuses on efforts to understand the microscopic origins of these signals and discusses how such coherences may be exploited to probe design principles of photosynthetic light harvesting.

Ab initiotheory of polarons: Formalism and applications

We develop a theoretical and computational framework to study polarons in semiconductors and insulators from first principles. Our approach provides the formation energy, excitation energy, and wavefunction of both electron and hole polarons, and takes into account the coupling of the electron or hole to all phonons. An important feature of the present method is that it does not require supercell calculations, and relies exclusively on electron band structures, phonon dispersions, and electron-phonon matrix elements obtained from calculations in the crystal unit cell. Starting from the Kohn-Sham (KS) equations of density-functional theory, we formulate the polaron problem as a variational minimization, and we obtain a nonlinear eigenvalue problem in the basis of KS states and phonon eigenmodes. In our formalism the electronic component of the polaron is expressed as a coherent superposition of KS states, in close analogy with the solution of the Bethe-Salpeter equation for the calculation of excitons. We demonstrate the power of the methodology by studying polarons in LiF and Li2O2. We show that our method describes both small and large polarons, and seamlessly captures Frohlich-type polar electron-phonon coupling and non-Frohlich coupling to acoustic and optical phonons. To analyze in quantitative terms the electron-phonon coupling mechanisms leading to the formation of polarons, we introduce spectral decompositions similar to the Eliashberg spectral function. We validate our theory using both analytical results and direct calculations on large supercells. This study constitutes a first step toward complete ab initio many-body calculations of polarons in real materials.

Quantum Computation Based on Quantum Adiabatic Bifurcations of Kerr-Nonlinear Parametric Oscillators

Quantum computers with Kerr-nonlinear parametric oscillators (KPOs) have recently been proposed by the author and others. Quantum computation using KPOs is based on quantum adiabatic bifurcations of the KPOs, which lead to quantum superpositions of coherent states, such as Schrodinger cat states. Therefore, these quantum computers are referred to as "quantum bifurcation machines (QbMs)." QbMs can be used for qauntum adiabatic optimization and universal quantum computation. Superconducting circuits with Josephson junctions, Josephson parametric oscillators (JPOs) in particular, are promising for physical implementation of KPOs. Thus, KPOs and QbMs offer not only a new path toward the realization of quantum bits (qubits) and quantum computers, but also a new application of JPOs. Here we theoretically explain the physics of KPOs and QbMs, comparing them with their dissipative counterparts. Their physical implementations with superconducting circuits are also presented.

Quantum correlations in qutrit-like superposition of spin coherent states

In this paper, we investigate quantum correlations in a qutrit-like superposition of spin coherent states. In particular, the quantum entanglement, the lower bound of the geometric measure of quantum discord, and the lower bound of local quantum uncertainty for the superposition of spin coherent states are examined, and their properties are characterized and compared. The specific dependence of these different correlation quantities on the spin of the system, the coefficient parameters, and the involved coherence parameters is found. As a part of this analysis, conditions for enhanced quantum correlations of qutrit-like superposition states have been identified, which exposes the characteristics of the states based on which the quantum correlations can be controlled and improved.

Quantum trajectories for environment in superposition of coherent states

We derive stochastic master equations for a quantum system interacting with a Bose field prepared in a superposition of continuous-mode coherent states. To determine a conditional evolution of the quantum system, we use a collision model with an environment given as an infinite chain of not interacting between themselves qubits prepared initially in an entangled state being a discrete analogue of a superposition of coherent states of the Bose field. The elements of the environment chain interact with the quantum system in turn one by one, and they are subsequently measured. We determine a conditional evolution of the quantum system for continuous in time observations of the output field as a limit of discrete recurrence equations. We consider the stochastic master equations for a counting as well as for a diffusive stochastic process.

New approach to the fidelity of quantum teleportation based on the entangled state generated by beam splitter

Entangled states play an important role in quantum computation and quantum information processing. Beam splitter, a linear device, is often used to prepare entangled states and quantum mechanics representations. For any two input states, the formula for the fidelity is derived, including the Q function representation, the P function representation, and the Wigner function representation, by using the output states from beam splitter as a source of quantum teleportation. This provides a new way to calculate the fidelity. As applications, two single-mode squeezed vacuum states and coherent superposition state together with coherent state are used as inputs, and the fidelity for teleporting coherent state is discussed. Our method provide more alternatives for calculating fidelity of teleportaion.

Coherent Superposition of Feshbach Dimers and Efimov Trimers.

A powerful experimental technique to study Efimov physics at positive scattering lengths is demonstrated. We use the Feshbach dimers as a local reference for Efimov trimers by creating a coherent superposition of both states. Measurement of its coherent evolution provides information on the binding energy of the trimers with unprecedented precision and yields access to previously inaccessible parameters of the system such as the Efimov trimers' lifetime and the elastic processes between atoms and the constituents of the superposition state. We develop a comprehensive data analysis suitable for noisy experimental data that confirms the trustworthiness of our demonstration.

Near-circularly polarized isolated attosecond pulse generation from coherent superposition state by a circularly polarized laser field

We theoretically investigate high-order harmonic generation (HHG) from a coherent superposition state of hydrogen atom in a circularly polarized (CP) laser field. The results show that, driven by the CP field, HHG from the coherent superposition state is enhanced by 4 to 5 orders of magnitude compared to that from the ground state. The enhanced intensity is comparable to that of the ground state in a linearly polarized laser field. Based on the classical and quantum analyses, we demonstrate that HHG in the CP laser field mainly arises from the recombination of electrons ionized at non-zero initial positions. The enhancement of HHG from the coherent superposition state is due to the higher ionization rate and also the larger probability density of electrons located far from the nucleus of the involved excited state. The obtained harmonic spectra support the generation of intense isolated attosecond pulses (IAPs) with the ellipticity as high as 0.93. Moreover, we show that the generation of IAPs with large ellipticity is robust against the variation of the carrier envelope phase (CEP) of the laser field. Our results provide a new route toward generating near-CP IAPs, which will be beneficial for ultrafast detection of chiral-sensitive light-matter interactions.

Quantum teleportation of qudits by means of generalized quasi-Bell states of light

Quantum superpositions of coherent states are produced both in microwave and optical domains, and are considered realizations of the famous “Schrödinger cat” state. The recent progress shows an increase in the number of components and the number of modes involved. Our work creates a theoretical framework for treatment of multicomponent two-mode Schrödinger cat states. We consider a class of single-mode states, which are superpositions of N coherent states lying on a circle in the phase space. In this class we consider an orthonormal basis created by rotationally-invariant circular states (RICS). A two-mode extension of this basis is created by splitting a single-mode RICS on a balanced beam-splitter. We show that these states are generalizations of Bell states of two qubits to the case of N-level systems encoded into superpositions of coherent states on the circle, and we propose for them the name of generalized quasi-Bell states. We show that using a state of this class as a shared resource, one can teleport a superposition of coherent states on the circle (a qudit). Differently from some other existing protocols of quantum teleportation, the proposed protocol provides the unit fidelity for all input states of the qudit. We calculate the probability of success for this type of teleportation and show that it approaches unity for the average number of photons in one component above N2. Thus, the teleportation protocol can be made unit-fidelity and deterministic at finite resources.

Transfer of quantum continuous variable states based on coupled resonator waveguide network

A high fidelity quantum transfer scheme for continuous variable states based on coupled resonator waveguide network is presented. We first give the transfer scheme of an arbitrary superposition of coherent states by using single coupled resonator waveguide, next we give the transfer scheme of entangled coherent states by using two parallel coupled resonator waveguides, and finally give the transfer scheme of continuous variable cluster states by using four parallel coupled resonator waveguides. The fidelity of all schemes is up to 100%.

Matter-wave interferometry with atoms in high Rydberg states

Matter-wave interferometry has been performed with helium atoms in high Rydberg states. In the experiments the atoms were prepared in coherent superpositions of Rydberg states with different electric dipole moments. Upon the application of an inhomogeneous electric field, the different forces on these internal state components resulted in the generation of coherent superpositions of momentum states. Using a sequence of microwave and electric field gradient pulses the internal Rydberg states were entangled with the momentum states associated with the external motion of these matter waves. Under these conditions matter-wave interference was observed by monitoring the populations of the Rydberg states as the magnitudes and durations of the pulsed electric field gradients were adjusted. The results of the experiments have been compared to, and are in excellent quantitative agreement with, matter-wave interference patterns calculated for the corresponding pulse sequences. For the Rydberg states used, the spatial extent of the Rydberg electron wavefunction was ∼320 nm. Matter-wave interferometry with such giant atoms is of interest in the exploration of the boundary between quantum and classical mechanics. The results presented also open new possibilities for measurements of the acceleration of Rydberg positronium or antihydrogen atoms in the Earth's gravitational field.

Obtaining phase-optimized states from superpositions of coherent states in phase-sensitive attenuating/amplifying reservoirs

In this paper we present new nonclassical states of a single mode of the electromagnetic field constructed by superpositions of coherent states distributed over a semi-straight line starting from the origin of the phase space. These states have highly concentrated phase distributions and can be useful as approximations of phase states. We propose feasible schemes to prepare such states in microwave high-Q cavities and as traveling modes. We investigate nonclassical properties and determine the Wigner functions of such pure states. Then we consider the system in contact with a reservoir, taking into account dissipation and gain processes in the Markovian approximation, and study the time-evolution of these states by solving the master equation in the Wigner representation. From explicit expressions of the time-dependent Wigner functions, we study the time-dependence of nonclassical properties and use the negativity of the Wigner function to analyze the disappearance of sub-Planck structures as time evolves.

Special functions with mod n symmetry and kaleidoscope of quantum coherent states

The set of mod n functions associated with primitive roots of unity and discrete Fourier transform is introduced. These functions naturally appear in description of superposition of coherent states related with regular polygon, which we call kaleidoscope of quantum coherent states. Displacement operators for kaleidoscope states are obtained by mod n exponential functions with operator argument and non-commutative addition formulas. Normalization constants, average number of photons, Heinsenberg uncertainty relations and coordinate representation of wave functions with mod n symmetry are expressed in a compact form by these functions.

Analytical Theory of Attosecond Transient Absorption Spectroscopy of Perturbatively Dressed Systems

A theoretical description of attosecond transient absorption spectroscopy for temporally and spatially overlapping XUV and optical pulses is developed, explaining the signals one can obtain in such an experiment. To this end, we employ a two-stage approach based on perturbation theory, which allows us to give an analytical expression for the transient absorption signal. We focus on the situation in which the attosecond XUV pulse is used to create a coherent superposition of electronic states. As we explain, the resulting dynamics can be detected in the spectrum of the transmitted XUV pulse by manipulating the electronic wave packet using a carrier-envelope-phase-stabilized optical dressing pulse. In addition to coherent electron dynamics triggered by the attosecond pulse, the transmitted XUV spectrum encodes information on electronic states made accessible by the optical dressing pulse. We illustrate these concepts through calculations performed for a few-level model.

Dynamics of Skew-Information and Bell’s Inequality Correlations for Two Coupled Dipole Qubits with 2-Photon Transition

We consider a dissipative system of two qubits interacting with a cavity field through the degenerate 2-photon transitions. The cavity is initially prepared in a superposition of coherent states. The non-classical correlations (NCCs) are investigated. Their robustness is analyzed by using the Skew information and the Bell’s non-locality. We show that the system presents stationary correlations and sudden birth entanglement. These phenomena depend crucially on the superposition of the coherent states, the dissipation rate and the dipole-dipole interaction parameters.

On-demand generation of traveling cat states using a parametric oscillator

We theoretically propose a method for on-demand generation of traveling Schr\"odinger cat states, namely, quantum superpositions of distinct coherent states of traveling fields. This method is based on deterministic generation of intracavity cat states using a Kerr-nonlinear parametric oscillator (KPO) via quantum adiabatic evolution. We show that the cat states generated inside a KPO can be released into an output mode by controlling the parametric pump amplitude dynamically. We further show that the quality of the traveling cat states can be improved by using a shortcut-to-adiabaticity technique.

Squeezing-enhanced superposition of coherent states and their nonclassical properties

We study the squeezing-enhanced superposition of coherent states, which are generated by operating a squeezing operator with two parameters on the superposition of coherent states with a different relative phase. The aim of this study is to discuss the nonclassical properties of these novel states by their quantum statistical and squeezing properties. The results show that the squeezing parameter r and relative phase θ play key roles in these states. It is clear to see that these new quantum states have stronger squeezing, antibunching effect, sub-Poissonian distributions behavior when compared to the normal squeezing superposition of coherent states.

Suppressed antibunching via spectral filtering: An analytical study in the two-photon Mollow regime

Mollow physics in the two-photon regime shows interesting features such as path-controlled time-reordering of photon pairs without the need to delay them. Here, we calculate analytically the two-photon correlations $ g^{(2)}(\tau)$, essential to discuss and study such phenomena in the resonant-driven dressed-state regime. It is shown that there exists upper and lower bounds of the $ g^{(2)}(\tau)-$ function for certain spectrally-selected photon pairs. Recent reported experiments agree with the presented theory and thereby it is shown that the resonant-driven four-level system is an interesting source for steerable quantum light in quantum cascade setups. We furthermore discuss the unlikeliness to observe antibunching for the delay time $ \tau=0 $ in the exciton-biexciton correlation functions in such experiments, since antibunching stems from a coherent and in-phase superposition of different photon emission events. Due to the occuring laser photon scattering, this coherent superposition state is easily disturbed and leads to correlation functions of $ g^{(2)}(0)=1$.