Superposition Of Coherent States Research Articles

Optimal circular states

Abstract In quantum optics, superpositions of coherent states, such as Schr"odinger cat states and compass states, and more generally, circular states, have attracted widespread attention due to their nice properties and significant applications. Concerning circular states, a natural question arises as what are the optimal parameters in these states for maximally achieving certain specified quantum features such as average photon number and nonclassicality. It turns out this issue is highly nontrivial and subtle. In this work, we investigate optimal circular states for average photon number, and determine the optimal parameters by a combination of theoretical and numerical methods. In particular, we establish several analytical results and also some rather detailed numerical results. We tabulate some numerical results, which may be useful in both theoretical and experimental studies of superpositions of coherent states.

Vector superstrata. Part II

Microstate geometries are proposed microstates of black holes which can be described within supergravity. Even though their number may not reproduce the full entropy of black holes with finite-sized horizons, they still offer a glimpse into the microscopic structure of black holes. In this paper we construct a new set of microstate geometries of the supersymmetric D1-D5-P black hole, where the momentum charge is carried by a vector field, as seen from the perspective of six-dimensional supergravity. To aid our construction, we develop an algorithm which solves a complicated partial differential equation using the regularity of the geometries. The new solutions are asymptotically AdS3 × S3, and have a long, but finite AdS2 throat that caps off without ever developing a horizon. These microstate geometries have a holographic interpretation as coherent superpositions of heavy states in the boundary D1-D5 CFT. We identify the states which are dual to our newly constructed solutions and carry out some basic consistency checks to support our identification.

Slowing Down a Coherent Superposition of Circular Rydberg States of Strontium.

Rydberg alkaline earth atoms are promising tools for quantum simulation and metrology. When one of the two valence electrons is promoted to long-lived circular states, the second valence electron can be optically manipulated without significant autoionization. We harness this feature to demonstrate laser slowing of a thermal atomic beam of circular strontium atoms. By driving the main ion core 422nm wavelength resonance, we observe a velocity reduction of 50 m/s without significant autoionization. We also show that a superposition of circular states undergoes very weak decoherence during the cooling process, up to the scattering of more than 1000 photons. This robustness opens new perspectives for quantum simulations over long timescales with circular atoms, while simultaneously cooling their motional state. It makes it possible to mitigate the harmful effects of unavoidable heating due to spin-motion coupling during a quantum simulation.

From Coherence to Function: Exploring the Connection in Chemical Systems.

ConspectusThe role of quantum mechanical coherences or coherent superposition states in excited state processes has received considerable attention in the last two decades largely due to advancements in ultrafast laser spectroscopy. These coherence effects hold promise for enhancing the efficiency and robustness of functionally relevant processes, even when confronted with energy disorder and environmental fluctuations. Understanding coherence deeply drives us to unravel mechanisms and dynamics controlled by order and synchronization at a quantum mechanical level, envisioning optical control of coherence to enhance functions or create new ones in molecular and material systems. In this frontier, the interplay between electronic and vibrational dynamics, specifically the influence of vibrations in directing electronic dynamics, has emerged as the leading principle. Here, two energetically disparate quantum degrees of freedom work in-sync to dictate the trajectory of an excited state reaction. Moreover, with the vibrational degree being directly related to the structural composition of molecular or material systems, new molecular designs could be inspired by tailoring certain structural elements.In the realm of chemical kinetics, our understanding of the dynamics of chemical transformations is underpinned by fundamental theories, such as transition state theory, activated rate theory, and Marcus theory. These theories elucidate reaction rates by considering the energy barriers that must be overcome for reactants to transform into products. Those barriers are surmounted by the stochastic nature of energy gap fluctuations within reacting systems, emphasizing that the reaction coordinate, the pathway from reactants to products, is not rigidly defined by a specific vibrational motion but encompasses a diverse array of molecular motions. While less is known about the involvement of specific intramolecular vibrational modes, their significance in certain cases cannot be overlooked.In this Account, we summarize key experimental findings that offer deeper insights into the complex electronic-vibrational trajectories encompassing excited states afforded from state-of-the-art ultrafast laser spectroscopy in three exemplary processes: photoinduced electron transfer, singlet-triplet intersystem crossing, and intramolecular vibrational energy flow in molecular systems. We delve into the rapid decoherence, or loss of phase and amplitude correlations, of vibrational coherences along promoter vibrations during subpicosecond intersystem crossing dynamics in a series of binuclear platinum complexes. This rapid decoherence illustrates the vibration-driven reactive pathways from the Franck-Condon state to the curve crossing region. We also explore the generation of new vibrational coherences induced by impulsive reaction dynamics rather than by the laser pulse in these systems, which sheds light on specific energy dissipation pathways and thereby on the progression of the reaction trajectory in the vicinity of the curve crossing on the product side. Another property of vibrational coherences, amplitude, reveals how energy can flow from one vibration to another in the electronic excited state of a terpyridine-molybdenum complex hosting a nonreactive dinitrogen substrate. A slight change in vibrational energy triggers a quasi-resonant interaction, leading to constructive wavepacket interference and ultimately intramolecular vibrational redistribution from a Franck-Condon active terpyridine vibration to a dinitrogen stretching vibration, energizing the dinitrogen bond.

Coherent control of rare earth 4f shell wavefunctions in the quantum spin liquid Tb2Ti2O7

The resonant excitation of electronic transitions with coherent laser sources creates quantum coherent superpositions of the involved electronic states. Most time-resolved studies have focused on gases or isolated subsystems embedded in insulating solids, aiming for applications in quantum information. Here, we focus on the coherent control of orbital wavefunctions in the correlated quantum material Tb2Ti2O7, which forms an interacting spin liquid ground state. We show that resonant excitation with a strong THz pulse creates a coherent superposition of the lowest energy Tb 4f states. The coherence manifests itself as a macroscopic oscillating magnetic dipole, which is detected by ultrafast resonant x-ray diffraction. We envision the coherent control of orbital wavefunctions demonstrated here to become a new tool for the ultrafast manipulation and investigation of quantum materials.

Quantum state engineering in a five-state chainwise system by generalized coincident pulse technique.

In this paper, an exact analytical solution is presented for achieving coherent population transfer and creating arbitrary coherent superposition states in a five-state chainwise system by a train of coincident pulses. We show that the solution of a five-state chainwise system can be reduced to an equivalent three-state Λ-type one with the simplest resonant coupling under the assumption of adiabatic elimination together with a requirement of the relation among the four coincident pulses. In this method, the four coincident pulses at each step all have the same time dependence, but with specific magnitudes. The results show that, by using a train of appropriately coincident pulses, this technique not only enables complete population transfer, but also creates any desired coherent superposition between the initial and final states, while the population in all intermediate states is effectively suppressed. Furthermore, this technique can also exhibit a one-way population transfer behavior. The results are of potential interest in applications where high-fidelity multi-state quantum control is essential, e.g., quantum information, atom optics, formation of ultracold molecules, cavity QED, nuclear coherent population transfer, and light transfer in waveguide arrays.

Entanglement and classical nonseparability convertible from orthogonal polarizations

The nonclassicality of a macroscopic single-mode optical superposition state is potentially convertible into entanglement, when the state is mixed with the vacuum on a beam splitter. Considering light beams with polarization degree of freedom in Euclidean space as coherent product states in a bipartite Hilbert space, we propose a method to convert the two orthogonal polarizations into simultaneous entanglement and classical nonseparability through nonclassicality in the superpositions of coherent and displaced Fock states. Equivalent Bell state emerges from the resulted superpositions and the proportion of mixed entanglement and nonseparablity is determined by the displacement amplitudes along the polarization directions. We characterize the state nonclassicality via features in Wigner distributions and propose an experimental method for generating these states and measuring them via homodyne tomography.

Passive continuous-variable quantum key distribution based on orthogonal frequency-division multiplexing in the terahertz band

We propose a passive continuous-variable quantum key distribution protocol based on multicarrier multiplexing technology in the terahertz band. In this paper, we realize the superposition of multipath coherent states by inverse Fourier transform and passive modulation. At the receiving end, the coherent states of the subcarriers are separated by quantum Fourier transform, and the keys are obtained in parallel by a homodyne (heterodyne) detector and post-processing. In addition, we derive the security bounds of the protocol and evaluate the performance in indoor environments and intersatellite links. Furthermore, we consider finite-size effects and propose tighter agreement constraints, which are more practical than those obtained in the asymptotic limit. This work will provide an effective way to build efficient wireless quantum communication networks.

Transfer of optical vortices in a coherently-prepared rare-earth-ion-doped solid

Optical vortices carrying orbital angular momentum (OAM) of light have earned much attention due to their potential applications in the classical and quantum physics. Quantum coherence has been proved to be an important tool for controlling the behavior of light fields. Developing the manipulation method of optical vortices is very useful for high-dimensional information processing encoded with OAM. In this paper, we experimentally investigate the transfer of optical vortices between different light modes in a coherently-prepared solid-state medium. Utilizing the technique of fractional stimulated Raman passage (f-STIRAP), the experimental medium is prepared into a coherent superposition of two ground states. By applying a probe vortex beam to scatter the induced atomic coherence, a new signal is generated with the same vorticity as that of the input probe field. Furthermore, the vortex beams are used as the f-STIRAP preparation pulses, and the helical phases of the vortex beams are mapped into the coherent superposition state. Subsequently, the optical vortices of the preparation pulses are transferred to a new light mode by using the probe beam to interact with the coherent medium. The new signal field accumulates the total topological charges of the applied fields in this coherent process. Such an experimental demonstration will enrich the interactions between optical vortices and matter, and can be helpful in further information processing.

Achieving quantum metrological performance and exact Heisenberg limit precision through superposition of s-spin coherent states

Achieving quantum metrological performance and exact Heisenberg limit precision through superposition of s-spin coherent states

Core-Hole Coherent Spectroscopy in Molecules.

We study the ultrafast dynamics initiated by a coherent superposition of core-excited states of nitrous oxide molecule. Using high-level abinitio methods, we show that the decoherence caused by the electronic decay and the nuclear dynamics is substantially slower than the induced ultrafast quantum beatings, allowing the system to undergo several oscillations before it dephases. We propose a proof-of-concept experiment using the harmonic up-conversion scheme available at x-ray free-electron laser facilities to trace the evolution of the created core-excited-state coherence through a time-resolved x-ray photoelectron spectroscopy.

Exciton migration in two-dimensional materials

Excitons play an essential role in the optical response of two-dimensional materials. These are bound states showing up in the band gaps of many-body systems and are conceived as quasiparticles formed by an electron and a hole. By performing real-time simulations in hBN, we show that an ultrashort (few-fs) UV pulse can produce a coherent superposition of excitonic states that induces an oscillatory motion of electrons and holes between different valleys in reciprocal space, leading to a sizeable exciton migration in real space. We also show that an ultrafast spectroscopy scheme based on the absorption of an attosecond pulse in combination with the UV pulse can be used to read out the laser-induced coherences, hence to extract the characteristic time for exciton migration. This work opens the door towards ultrafast electronics and valleytronics adding time as a control knob and exploiting electron coherence at the early times of excitation.

Fermion-parity qubit in a proximitized double quantum dot

Bound states in quantum dots coupled to superconductors can be in a coherent superposition of states with different electron number but with the same fermion parity. Electrostatic gating can tune this superposition to a sweet spot, where the quantum dot has the same mean electric charge independent of its electron-number parity. Here, we propose to encode quantum information in the local fermion parity of two tunnel-coupled quantum dots embedded in a Josephson junction. At the sweet spot, the qubit states have zero charge dipole moment. This protects the qubit from dephasing due to charge noise acting on the potential of each dot, as well as fluctuations of the (weak) interdot tunneling. At weak interdot tunneling, relaxation is suppressed because of disjoint qubit states. However, for strong interdot tunneling the system is protected against noise affecting each quantum dot separately (energy-level noise, dot-superconductor tunneling fluctuations, and hyperfine interactions). Finally, we describe initialization and readout as well as single-qubit and two-qubit gates by pulsing gate voltages. Published by the American Physical Society 2024

Studying phonon coherence with a quantum sensor

Nanomechanical oscillators offer numerous advantages for quantum technologies. Their integration with superconducting qubits shows promise for hardware-efficient quantum error-correction protocols involving superpositions of mechanical coherent states. Limitations of this approach include mechanical decoherence processes, particularly two-level system (TLS) defects, which have been widely studied using classical fields and detectors. In this manuscript, we use a superconducting qubit as a quantum sensor to perform phonon number-resolved measurements on a piezoelectrically coupled phononic crystal cavity. This enables a high-resolution study of mechanical dissipation and dephasing in coherent states of variable size (n¯≃1−10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{n}\\simeq 1-10$$\\end{document} phonons). We observe nonexponential relaxation and state size-dependent reduction of the dephasing rate, which we attribute to TLS. Using a numerical model, we reproduce the dissipation signatures (and to a lesser extent, the dephasing signatures) via emission into a small ensemble (N = 5) of rapidly dephasing TLS. Our findings comprise a detailed examination of TLS-induced phonon decoherence in the quantum regime.

Super-resolution and super-sensitivity of quantum LiDAR with a multi-photonic state and binary outcome photon counting measurement

Here, we are investigating the enhancement in resolution and phase sensitivity of a Mach-Zehnder interferometer (MZI) based quantum LiDAR. We are using a multi-photonic state (MPS), superposition of four coherent states [Int. J. Quantum Inf. 19, 2150013 (2021)0219-749910.1142/S0219749921500131], as the input state and binary outcome parity photon counting measurement and binary outcome zero non-zero photon counting measurement as the measurement schemes. We have thoroughly investigated the results in lossless as well as lossy cases. We found enhancement in resolution and phase sensitivity in comparison to the coherent state and even coherent superposition state (ECSS) based quantum LiDAR. Our analysis shows that MPS may be an alternative nonclassical resource in the field of quantum imaging and quantum sensing technologies, like in quantum LiDAR.

A unified theory of tunneling times promoted by Ramsey clocks.

What time does a clock tell after quantum tunneling? Predictions and indirect measurements range from superluminal or instantaneous tunneling to finite durations, depending on the specific experiment and the precise definition of the elapsed time. Proposals and implementations use the atomic motion to define this delay, although the inherent quantum nature of atoms implies a delocalization and is in sharp contrast to classical trajectories. Here, we rely on an operational approach: We prepare atoms in a coherent superposition of internal states and study the time read-off via a Ramsey sequence after the tunneling process without the notion of classical trajectories or velocities. Our operational framework (i) unifies definitions of tunneling delay within one approach, (ii) connects the time to a frequency standard given by a conventional atomic clock that can be boosted by differential light shifts, and (iii) highlights that there exists no superluminal or instantaneous tunneling.

Coherent x-ray spontaneous emission spectroscopy of conical intersections.

Conical intersections are known to play a vital role in many photochemical processes. The breakdown of the Born-Oppenheimer approximation in the vicinity of a conical intersection causes exciting phenomena, such as the ultrafast radiationless decay of excited states. The passage of a molecule through a conical intersection creates a coherent superposition of electronic states via nonadiabatic couplings. Detecting this coherent superposition may serve as a direct probe of the conical intersection. In this paper, we theoretically demonstrate the use of coherent spontaneous emission in samples with long-range order for probing the occurrence of a conical intersection in a molecule. Our simulations show that the spectrum contains clear signatures of the created coherent superposition of electronic states. We investigate the bandwidth requirements for the x-ray probes, which influence the observation of coherent superposition generated by the conical intersection.

Elastic bit and Berry phase: Investigating topological phenomena in a classical granular network

This study investigates the Berry phase, a key concept in classical and quantum physics, and its manifestation in a classical system. We achieve controlled accumulation of the Berry phase by manipulating the elastic bit (a classical analogue to a quantum bit) in an externally driven, homogeneous, spherical, nonlinear granular network. This is achieved through the classical counterpart of quantum coherent superposition of states. The elastic bit's state vectors are navigated on the Bloch sphere using external drivers' amplitude, phase, and frequency, yielding specific Berry phases. These phases distinguish between trivial and nontrivial topologies of the elastic bit, with the zero Berry phase indicating pure states of the linearized granular system and the nontrivial π phase representing equal superposed states. Other superposed states acquire different Berry phases. Crucially, these phases correlate with the structure's eigenmode vibrations: trivial phases align with distinct, in-phase, or out-of-phase eigenmodes, while nontrivial phases correspond to coupled vibrations where energy is shared among granules, alternating between oscillation and rest. Additionally, we explore Berry's phase generalizations for non-cyclic evolutions. This research paves the way for advanced quantum-inspired sensing and computation applications by utilizing and controlling the Berry phase.

Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states.

Advances in coherent light sources and development of pump-probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron-nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. This work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes.

Second-scale rotational coherence and dipolar interactions in a gas of ultracold polar molecules

Ultracold polar molecules combine a rich structure of long-lived internal states with access to controllable long-range anisotropic dipole–dipole interactions. In particular, the rotational states of polar molecules confined in optical tweezers or optical lattices may be used to encode interacting qubits for quantum computation or pseudo-spins for simulating quantum magnetism. As with all quantum platforms, the engineering of robust coherent superpositions of states is vital. However, for optically trapped molecules, the coherence time between rotational states is typically limited by inhomogeneous differential light shifts. Here we demonstrate a rotationally magic optical trap for 87Rb133Cs molecules that supports a Ramsey coherence time of 0.78(4) s in the absence of dipole–dipole interactions. This is estimated to extend to >1.4 s at the 95% confidence level using a single spin-echo pulse. In our trap, dipolar interactions become the dominant mechanism by which Ramsey contrast is lost for superpositions that generate oscillating dipoles. By changing the states forming the superposition, we tune the effective dipole moment and show that the coherence time is inversely proportional to the strength of the dipolar interaction. Our work unlocks the full potential of the rotational degree of freedom in molecules for quantum computation and quantum simulation.