First-order Correlation Function Research Articles

Dynamics and resonance fluorescence from a superconducting artificial atom doubly driven by quantized and classical fields

We report an experimental demonstration of resonance fluorescence in a two-level superconducting artificial atom under two driving fields coupled to a detuned cavity. One of the fields is classical and the other is varied from quantum (vacuum fluctuations) to classical by controlling the photon number inside the cavity. The device consists of a transmon qubit strongly coupled to a one-dimensional transmission line and a coplanar waveguide resonator. We observe a sideband anticrossing and asymmetry in the emission spectra of the system through a one-dimensional transmission line, which is fundamentally different from the weak-coupling case. By changing the photon number inside the cavity, the emission spectrum of our doubly driven system approaches the case when the atom is driven by two classical bichromatic fields. We also measure the dynamical evolution of the system through the transmission line and study the properties of the first-order correlation function, Rabi oscillations, and energy relaxation in the system. The study of resonance fluorescence from an atom driven by two fields promotes understanding decoherence in superconducting quantum circuits and may find applications in superconducting quantum computing and quantum networks. Published by the American Physical Society 2024

Anomalous cooling of bosons by dimensional reduction.

Cold atomic gases provide a remarkable testbed to study the physics of interacting many-body quantum systems. Temperatures are necessarily nonzero, but cooling to the ultralow temperatures needed for quantum simulation purposes or even simply measuring the temperatures directly on the system can prove to be very challenging tasks. Here, we implement thermometry on strongly interacting two- and one-dimensional Bose gases with high sensitivity in the nanokelvin temperature range. Our method is aided by the fact that the decay of the first-order correlation function is very sensitive to the temperature when interactions are strong. We find that there may be a substantial temperature variation when the three-dimensional quantum gas is cut into two-dimensional slices or into one-dimensional tubes. Notably, the temperature for the one-dimensional case can be much lower than the initial temperature. Our findings show that this decrease results from the interplay of dimensional reduction and strong interactions.

Vortices in multilayer stacks of Bose–Einstein condensates with tilted dipoles

In this paper, we consider the formation of vortices in multilayer stacks of Bose–Einstein condensates with tilted dipoles by numerical simulations of the Gross–Pitaevskii equation. Different dependencies of critical rotation frequency (CRF) and optical lattice height, vortex number, and rotation frequency are studied, depending on the direction of the dipole axis and dipole strength. Our results show that the CRF in z = 0 is minimum. When the optical lattice height is gradually increased, the CRF decreases gradually. Reducing of dipole strength in anisotropic dipole–dipole interaction (DDI) favours the formation of vortices, and such decline in isotropic DDI hinders the creation of vortices. The reason for this difference is that the repulsive interaction is favorable and the attractive interaction is disadvantageous for the vortex formation. In addition, we study the first-order correlation function and focus on variation of coherence. For small rotation frequency, the break of coherence occurs earlier in the case of purely repulsive interaction. With an increase in rotation frequency, the coherence concurrently disappears in layer z = 2. Moreover, we also investigate the quenched dynamics, showing that the increase of angular momentum is induced by changing the direction of dipoles and in this process the vortex number remains unchanged.

Modified Mach-Zehnder interferometer for spatial coherence measurement.

Spatial coherence of light sources is usually obtained by using the classical Young's interferometer. Although the original experiment was improved upon in successive works, some drawbacks still remain. For example, several pairs of points must be used to obtain the complex coherence degree (normalized first-order correlation function) of the source. In this work, a modified Mach-Zehnder interferometer which includes a pair of lenses and is able to measure the spatial coherence degree is presented. With this modified Mach-Zehnder interferometer, it is possible to measure the full 4D spatial coherence function by displacing the incoming beam laterally. To test it, we have measured only a 2D projection (zero shear) of the 4D spatial coherence, which is enough to characterize some types of sources. The setup has no movable parts, making it robust and portable. To test it, the two-dimensional spatial coherence of a high-speed laser with two cavities was measured for different pulse energy values. We observe from the experimental measurements that the complex degree of coherence changes with the selected output energy. Both laser cavities seem to have similar complex coherence degrees for the maximum energy, although it is not symmetrical. Thus, this analysis will allow us to determine the best configuration of the double-cavity laser for interferometric applications. Furthermore, the proposed approach can be applied to any other light sources.

Single photons versus coherent-state input in waveguide quantum electrodynamics: Light scattering, Kerr, and cross-Kerr effect

While the theoretical studies in waveguide quantum electrodynamics predominate with single-photon and two-photon Fock-state (photon number states) input, the experiments are primarily carried out using a faint coherent light. We create a theoretical toolbox to compare and contrast linear and nonlinear light scattering by a two-level or a three-level emitter embedded in an open waveguide carrying Fock-state or coherent-state inputs. We particularly investigate light transport properties and the Kerr and cross-Kerr nonlinearities of the medium for the two types of inputs. A generalized description of the Kerr and cross-Kerr effect for different types of inputs is formulated using the first-order correlation function to compare the Kerr and cross-Kerr nonlinearity between two photons in these models.

Kardar-Parisi-Zhang universality in discrete two-dimensional driven-dissipative exciton polariton condensates

The statistics of the fluctuations of quantum many-body systems are highly revealing of their nature. In driven-dissipative systems displaying macroscopic quantum coherence, as exciton polariton condensates under incoherent pumping, the phase dynamics can be mapped to the stochastic Kardar-Parisi-Zhang (KPZ) equation. However, in two dimensions (2D), it was theoretically argued that the KPZ regime may be hindered by the presence of vortices, and a non-equilibrium BKT behavior was reported close to condensation threshold. We demonstrate here that, when a discretized 2D polariton system is considered, universal KPZ properties can emerge. We support our analysis by extensive numerical simulations of the discrete stochastic generalized Gross-Pitaevskii equation. We show that the first-order correlation function of the condensate exhibits stretched exponential behaviors in space and time with critical exponents characteristic of the 2D KPZ universality class, and find that the related scaling function accurately matches the KPZ theoretical one, stemming from functional Renormalization Group. We also obtain the distribution of the phase fluctuations and find that it is non-Gaussian, as expected for a KPZ stochastic process.

Photon correlation spectroscopy with heterodyne mixing based on soft x-ray magnetic circular dichroism

Many magnetic equilibrium states and phase transitions are characterized by fluctuations. Such magnetic fluctuation can in principle be detected with scattering-based x-ray photon correlation spectroscopy (XPCS). However, in the established approach of XPCS, the magnetic scattering signal is quadratic in the magnetic scattering cross section, which results not only in often prohibitively small signals but also in a fundamental inability to detect negative correlations (anticorrelations). Here, we propose to exploit the possibility of heterodyne mixing of the magnetic signal with static charge scattering to reconstruct the first-order (linear) magnetic correlation function. We show that the first-order magnetic scattering signal reconstructed from heterodyne scattering now directly represents the underlying magnetization texture. Moreover, we suggest a practical implementation based on an absorption mask rigidly connected to the sample, which not only produces a static charge scattering signal but also eliminates the problem of drift-induced artificial decay of the correlation functions. Our method thereby significantly broadens the range of scientific questions accessible by magnetic x-ray photon correlation spectroscopy.

Revealing the Orbital Angular Momentum Spectrum and Correlation Phase of Optical Vortices With Wander Perturbations and Spiral Offsets

Controlling the orbital angular momentum (OAM) spectrum, as well as the modulus and phase of the first-order correlation function of a vortex beam produced by a dynamic wander source, is critical for the use of OAM photons in turbulent environments. Based on a derived analytical formula for the first-order correlation function of the light field, a theoretical model and an experimental approach are proposed for synthesizing and detecting complex wander vortex beams in the laboratory. Wander perturbations and spiral phase offsets are considered. The correlation phase and OAM spectrum of complex wander vortex beams are measured with a single spatial light modulator (SLM). The experimental results agree with the theoretical simulations and show that, given a limited region of interest, wander perturbations broaden the OAM spectrum asymmetrically with respect to the initial input mode, with a higher proportion of lower ordered non-signal modes than higher ordered modes. For a large spiral phase offset, the main peak of the OAM spectrum shifts away from the signal mode and toward a lower ordered side mode. Generation and measurement strategies have significant potential for free-space communication and remote sensing in turbulent environments.

The time-dependent polaron frame

The single-photon emitters in solid-state photonic devices have become crucial for quantum technology implementations. The exciton–phonon interaction degrades the quality of the photons even when the coherent scattering is dominant. Some models describing an emitter’s trajectory in a phonon bath are the weak-coupling master equation and the standard and variational polaron master equations. The polaron theory based on a steady polaron transformation cannot capture the response of the phonon reservoir upon the exciton creation in its transformed Hamiltonian. Here, a time-dependent phonon displacement leads to the time evolution of the phonon-related energies and correlations. Variables as the phonon-induced energy shift and the phonon first-order correlation function converge to the standard polaron theory results. However, the expectation value of the phonon displacement operator differs. According to the time-dependent polaron master equation, the mitigation of the coupling between the single-photon emitter and the coherent driving field by the phonon reservoir evolves to be worse than predicted in the standard polaron theory. • A time-dependent polaron unitary transformation is derived • Time evolution of the exciton–phonon interaction • The path from the weak-coupling Hamiltonian to the polaron Hamiltonian

Mirror-assisted backscattering interferometry to measure the first-order correlation function of the light emitted by quantum scatterers

We present a new method to obtain the first-order temporal correlation function, $g^{(1)} (\tau)$, of the light scattered by an assembly of point-like quantum scatterers, or equivalently its spectral power distribution. This new method is based on the mirror-assisted backscattering interferometric setup. The contrast of its angular fringes was already linked in the past to the convolution of $g^{(1)} (\tau)$ for different Rabi frequencies taking into account the incoming spatial intensity profile of the probe beam, but we show here that by simply adding a half waveplate to the interferometer in a specific configuration, the fringe contrast becomes $g^{(1)} (\tau)$ of the light scattered by atoms, which are now all subjected to the same laser intensity. This new method has direct application to obtain the saturated spectrum of quantum systems. We discuss some non-trivial aspects of this interferometric setup, and propose an analogy with a double Mach-Zehnder interferometer.

Multi-Particle Interference in an Electronic Mach-Zehnder Interferometer.

The development of dynamic single-electron sources has made it possible to observe and manipulate the quantum properties of individual charge carriers in mesoscopic circuits. Here, we investigate multi-particle effects in an electronic Mach–Zehnder interferometer driven by a series of voltage pulses. To this end, we employ a Floquet scattering formalism to evaluate the interference current and the visibility in the outputs of the interferometer. An injected multi-particle state can be described by its first-order correlation function, which we decompose into a sum of elementary correlation functions that each represent a single particle. Each particle in the pulse contributes independently to the interference current, while the visibility (given by the maximal interference current) exhibits a Fraunhofer-like diffraction pattern caused by the multi-particle interference between different particles in the pulse. For a sequence of multi-particle pulses, the visibility resembles the diffraction pattern from a grid, with the role of the grid and the spacing between the slits being played by the pulses and the time delay between them. Our findings may be observed in future experiments by injecting multi-particle pulses into a Mach–Zehnder interferometer.

Stellar Speckle and Correlation Derived From Classical Wave Expansions for Spherical Antennas

Michelson phase and Hanbury Brown-Twiss intensity stellar interferometry require expressions for the first-and second-order correlation functions, respectively, of the fields radiated by stars in terms of their diameters and measured quasi-monochromatic wavelengths. Although our sun and most other stars are spherical in shape at optical wavelengths, previous determinations of speckle and correlation functions have modeled stars as circular disks rather than spheres because of the mathematical tools available for partially coherent fields on planar surfaces. However, with the incentive that most stars are indeed shaped like spheres and not disks, this article models a star as a spherical antenna composed of a random distribution of uncorrelated volume sources within a thin surface layer (photosphere). Working directly with the time-domain fields, a self-contained, straightforward, detailed derivation of speckle patterns and correlation functions is given based on a novel, angularly symmetric, spherical mode expansion with coefficients determined by the assumed Lambertian nature of the star's radiation and the uniform asymptotic behavior of the spherical Hankel functions. First-order spatially averaged and temporally averaged correlation functions are proven to be identical, and the normalized second-order correlation function is shown to equal one plus the square of the first-order correlation function. The direct time-domain approach reveals explicit expressions for the quasi-monochromatic wave-packet fields of stellar radiation as well as new criteria for the validity of the far-field approximation for the fields of incoherent sources that are much less restrictive than the Rayleigh-distance criterion for coherent sources.

Superfluidity and coherence in uniform dipolar binary Bose mixtures

We investigate the superfluidity and the coherence in dipolar binary Bose mixtures using the hydrodynamic approach. Useful analytical formulas for the excitation spectra, the first-order correlation function, the static structure factor, and the superfluid fraction are derived. We find that in the case of highly imbalanced mixture, the superfluidity can occur in the dilute component only at extremely low temperatures. The behavior of the first-order correlation function for both dipolar and nondipolar Bose mixtures is deeply analyzed. Then we face the two-dimensional case which encodes a non-trivial physics due to the roton modes.

Quantum analysis of a traveling-wave electro-optic phase modulator in the presence of the phase noise from a radio frequency oscillator and a laser

Quantum analysis has been done for the traveling-wave (TW) electro-optic phase modulator in the presence of the phase noise of a radio frequency (RF) oscillator and a laser source, in which the Hamiltonian for an active section of the phase modulator system is derived. The effect of RF phase noise from the oscillator and a phase velocity mismatch (PVM) between optical photons and the RF field are included in the Hamiltonian. The time evolution of the field operator of the laser in the TW electro-optic phase modulator is derived by the Heisenberg equation of motion. The action of a TW electro-optic phase modulator in the presence of the two distinct weak noises—classical phase noise because of RF and quantum phase noise caused by a laser—has been evaluated and explained in terms of the second-order temporal correlation function and power spectrum. The power spectrum has been written as a function of the semiconductor laser linewidth, an enhancement factor in the laser linewidth, and the RF oscillator linewidth. The results are applied to analyze the basic model of a frequency-coded quantum key distribution (FC-QKD) system. The quantum bit error rate (QBER), the first-order optical intensity correlation function, and the spectrum of intensity fluctuation have been calculated for the partially coherent regime to evaluate the performance of the FC-QKD system.

Relaxation of Shannon entropy for trapped interacting bosons with dipolar interactions

We study the quantum many-body dynamics and entropy production triggered by an interaction quench of few dipolar bosons in an external harmonic trap. We solve the time-dependent many-body Schrödinger equation by using an in-principle numerically exact many-body method called the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We study the dynamical measures with high level of accuracy. We monitor the time evolution of the occupation in the natural orbitals and normalized first- and second-order Glauber’s correlation functions. In particular, we focus on the relaxation dynamics of the Shannon entropy. Comparison with the corresponding results for contact interactions is presented. We observe significant effects coming from the presence of the non-local part of the dipolar interaction. The relaxation process is very fast for dipolar bosons with a clear signature of a truly saturated maximum entropy state. We also discuss the connection between the entropy production and the occurrence of correlations and loss of coherence in the system. We identify the long-time relaxed state as a many-body state retaining only diagonal correlations in the first-order correlation function and building up anti-bunching effect in the second-order correlation function.

Excitation spectrum and supersolidity of a two-leg bosonic ring ladder

We consider a system of weakly interacting bosons confined on a planar double lattice ring subjected to two artificial gauge fields. This system is known to display three phases, the Meissner phase where the flow of particles is carried at the edges of the system without transverse current, a vortex phase characterized by non-zero transverse current, and a biased-ladder phase, characterized by an imbalance of the population of the two rings. We use the Bogoliubov approximation to determine the excitation spectrum in the three phases, the dynamic structure factor and the quantum fluctuation corrections to the first-order correlation function. Our analysis reveals supersolid features as well as Josephson modes, corresponding to out-of-phase modes of the finite ring.

Dynamical Properties of the Finite-size Dicke Model Coupled to a Thermal Reservoir

We investigate the dynamical properties of the finite-size Dicke model coupled to a photon reservoir in the dispersive regime. The system-reservoir coupling in our Hamiltonian includes counter-rotating terms, which are relevant in the strong atom-cavity coupling. Because the dispersive regime is considered, the dynamics of low-energy states are described sufficiently accurately within the finite-dimensional subspace of the dressed states. Using the separation of the time scales between the system and the reservoir, we derive the Markovian quantum master equation in the subspace without ignoring the counter-rotating terms. The temporal evolution of the expectation of the cavity mode shows that the bifurcation of the long-lived state corresponds to the superradiant transition in the isolated model. The master equation explicitly gives the steady state solution. The numerical results for the first-order correlation function on the steady state indicate that the strong atom-cavity coupling enhances the coherence and softens the dephasing in the superradiant region.

Grating Lobes in Higher-Order Correlation Functions of Arrays of Quantum Emitters: Directional Photon Bunching Versus Correlated Directions

Recent advances in nanofabrication and optical manipulation techniques are making it possible to build arrays of quantum emitters with accurate control over the locations of their individual elements. In analogy with classical antenna arrays, this poses new opportunities for tailoring quantum interference effects by designing the geometry of the array. Here, we investigate the N th -order directional correlation function of the photons emitted by an array of N initially-excited identical quantum emitters, addressing the impact of the appearance of grating lobes. Our analysis reveals that the absence of directivity in the first-order correlation function is contrasted by an enhanced directivity in the N th -order one. This suggests that the emitted light consists of a superposition of directionally entangled photon bunches. Moreover, the photon correlation landscape changes radically with the appearance of grating lobes. In fact, the photons no longer tend to be bunched along the same direction; rather, they are distributed in a set of correlated directions with equal probability. These results clarify basic aspects of light emission from ensembles of quantum emitters. Furthermore, they may find applications in the design of nonclassical light sources.

Nonequilibrium polariton dynamics in a Bose-Einstein condensate coupled to an optical cavity

We study quasiparticle scattering effects on the dynamics of a homogeneous Bose-Einstein condensate of ultracold atoms coupled to a single mode of an optical cavity. The relevant excitations, which are polaritonlike mixed excitations of photonic and atomic density-wave modes, are identified. All the first-order correlation functions are presented by means of the Keldysh Green's function technique. Beyond confirming the existence of the resonant enhancement of Beliaev damping, we find a very structured spectrum of fluctuations. There is a spectral hole burning at half of the recoil frequency reflecting the singularity of the Beliaev scattering process. The effects of the photon-loss dissipation channel and that of the Beliaev damping due to atom-atom collisions can be well separated. We show that the Beliaev process does not influence the properties of the self-organization criticality.

Rapid and Quantitative De-tert-butylation for Poly(acrylic acid) Block Copolymers and Influence on Relaxation of Thermoassociated Transient Networks.

The synthesis of charged polymers often requires the polymerization of protected monomers, followed by a polymer-analogous reaction to the polyelectrolyte product. We present a mild, facile method to cleave tert-butyl groups from poly(tert-butyl acrylate) blocks that yields poly(acrylic acid) (pAA) blocks free of traces of the ester. The reaction utilizes a slight excess of HCl in hexafluoroisopropanol (HFIP) at room temperature and runs to completion within 4 h. We compare deprotection in HFIP with the common TFA/DCM method and show that the latter does not yield clean pAA. We show the effect of complete tert-butyl cleavage on a ABA triblock copolymer, where poly(N-isopropylacrylamide) (pNIPAM) is A and pAA is B, by means of viscosimetry, DLS, and SAXS on solutions above overlap. The pNIPAM blocks dehydrate, and their increased self-affinity above the lower critical solution temperature (LCST) results in network formation by the triblocks. This manifests itself as an increase in viscosity and a slowing down of the first-order correlation function in light scattering. However, this stickering effect manifests itself exclusively when the pAA block is tert-butyl-free. Additionally, SAXS shows that the conformational properties of tert-butyl-free pAA copolymers are markedly different from those with residual esters. Thus, we illustrate a surprising effect of hydrophobic impurities that act across blocks and assert the usefulness of HCl/HFIP in pAA synthesis.