Thermal Coherent State Research Articles

Beating the spectroscopic Rayleigh limit via post-processed heterodyne detection.

Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered measurements. An alternative to complex experimental setups is to use simple homodyne detection and customized data analysis. We experimentally investigate this method in the time-frequency domain and demonstrate the spectroscopic superresolution for two distinct types of light sources: thermal and phase-averaged coherent states. The experimental results are backed by theoretical predictions based on estimation theory.

Quantum Otto heat engine with Pöschl–Teller potential in contact with coherent thermal bath

Work and efficiency of quantum Otto heat engines (QOHEs) can increase by using non-thermal baths or by inhomogeneous scaling of energy levels of the working substance. Given these points, at first, we construct the coherent thermal state for a trigonometric Pöschl–Teller (PT) potential. Then using a particle in this potential, which has unequally spaced energy levels, as a working substance, we investigate the work extraction and the efficiency of QOHEs that operates between cold and hot coherent thermal baths. The results show that changing the PT potential parameters in the adiabatic processes of QOHE, which causes an inhomogeneous shift in energy levels or/and make use of the hot coherent thermal bath, improve work extraction and efficiency of QOHE relative to the classical counterpart.

Leggett-Garg violations for continuous-variable systems with Gaussian states

Macrorealism (MR) is the worldview that certain quantities may take definite values at all times irrespective of past or future measurements and may be experimentally falsified via the Leggett-Garg (LG) inequalities. We put this worldview to the test for systems described by a continuous variable $x$ by seeking LG violations for measurements of a dichotomic variable $Q=\text{sign}(x)$, in the case of Gaussian initial states in a quantum harmonic oscillator. Extending our earlier analysis [C. Mawby and J. J. Halliwell, Phys. Rev. A 105, 022221 (2022)], we find analytic expressions for the temporal correlators. An exploration of parameter space reveals significant regimes in which the two-time LG inequalities are violated, and likewise at three and four times. To obtain a physical picture of the LG violations, we exploit the continuous nature of the underlying position variable and analyze the relevant quantum-mechanical currents, Bohm trajectories, and Wigner function. We also show that larger violations are possible using the Wigner LG inequalities. Further, we extend the analysis to LG tests using coherent state projectors, thermal coherent states, and squeezed states.

Quantum metrology with multimode Gaussian states of multiple point sources

A unified theoretical framework is developed for measuring multimode Gaussian states of multiple point sources. The spatial and temporal mode functions are found analytically by aid of the circular symmetry of the object plane and aperture, as well as by the rectangular spectral density function of the background. They relate the modal operators and statistical moments to the locations of the point sources through the prolate spheroidal functions. An experimentally straightforward implementation is proposed, which consists of a nonabsorptive polarization- and phase-modulating spatial light modulator (SLM), three lenses, and a polarization beam splitter. Interestingly, it is found that the spatial modal annihilation operators are related to the modal field operators in the image plane by a simple complex-valued scale factor. The quantum Fisher information matrix and quantum Cram\'er-Rao bound (QCRB) are also discussed. The numerical calculation of QCRB is completed for the case where the spatially multimode aperture fields are prepared by the spatial propagation from temporally single-mode thermal states, coherent states, or quadrature squeezed states of the point sources in the object plane. The results show that the Rayleigh limit can always be surpassed by means of increasing the mean photon rate or the squeeze parameter.

Energetic Cost of Measurements Using Quantum, Coherent, and Thermal Light.

Quantum measurements are basic operations that play a critical role in the study and application of quantum information. We study how the use of quantum, coherent, and classical thermal states of light in a circuit quantum electrodynamics setup impacts the performance of quantum measurements, by comparing their respective measurement backaction and measurement signal to noise ratio per photon. In the strong dispersive limit, we find that thermal light is capable of performing quantum measurements with comparable efficiency to coherent light, both being outperformed by single-photon light. We then analyze the thermodynamic cost of each measurement scheme. We show that single-photon light shows an advantage in terms of energy cost per information gain, reaching the fundamental thermodynamic cost.

Estimation of light-matter coupling constant under dispersive interaction based on quantum Fisher information

Quantum parameter estimation is one of the most important applications in quantum metrology. The basic theory of quantum parameter estimation－quantum Cramer-Rao bound－shows that the precision limit of quantum parameter estimation is directly related to quantum Fisher information. Therefore quantum Fisher information is extremely important in the quantum parameter estimation. In this paper we use quantum parameter estimation theory to estimate the coupling constant of the Jaynes-Cummings model with large detuning. The initial probing state is the direct product state of qubit and radiation field in which Fock state, thermal state and coherent state are taken into account respectively. We calculate the quantum Fisher information of the hybrid system as well as qubit and radiation field for each probing state after the parameter evolution under the Hamiltonian of the Jaynes-Cummings model with large detuning. The results show that the quantum Fisher information increases monotonically with the average photon number increasing. The optimal detection state is that when the qubit system is in the equal weight superposition of the ground and the excited state, at this time the quantum Fisher information always reaches a maximum value, When the radiation field of probing state is Fock state or the thermal state, the information about the estimated parameter is included only in the qubit. The estimation accuracy of the coupling constant with thermal state or coherent state is higher than that with Fock state.

Dynamics of field nonclassicality in the Jaynes–Cummings model

Employing an informational quantifier for nonclassicality of bosonic field based on the Wigner–Yanase skew information, we investigate the dynamics of field nonclassicality in the Jaynes–Cummings model evolving from several typical initial atom–field states: coherent states, Fock states, and thermal states for the field, and ground state, excited state, symmetric superposition state, and maximally mixed state for the atom. We reveal some intriguing features of the field dynamics and their sensitivity on the initial states from an informational perspective. The results show that field nonclassicality can be generated in most cases and exhibits complex dynamic patterns involving collapses and revivals. A remarkable observation is that the initial coherent field states, assisted by the atom, can be converted to almost maximally nonclassical field states constrained by the average photon number, even though all coherent states are the most classical and possess the same minimal nonclassicality among pure states. The field dynamics may be exploited to estimate the initial atom as well as the field states, prepare desired evolving states and process quantum information.

Quantum field theory with dynamical boundary conditions and the Casimir effect: coherent states *

We have studied in a previous work the quantization of a mixed bulk-boundary system describing the coupled dynamics between a bulk quantum field confined to a spacetime with finite space slice and with timelike boundary, and a boundary observable defined on the boundary. Our bulk system is a quantum field in a spacetime with timelike boundary and a dynamical boundary condition—the boundary observable’s equation of motion. Owing to important physical motivations, in such previous work we have computed the renormalized local state polarization and local Casimir energy for both the bulk quantum field and the boundary observable in the ground state and in a Gibbs state at finite, positive temperature. In this work, we introduce an appropriate notion of coherent and thermal coherent states for this mixed bulk-boundary system, and extend our previous study of the renormalized local state polarization and local Casimir energy to coherent and thermal coherent states. We also present numerical results for the integrated Casimir energy and for the Casimir force.

Quantum speed limit in the thermal spin-boson system with and without tunneling term

In this paper, we study the spin-bosonic model, with and without tunneling terms, in detail. The spin-bosonic model without tunneling is studied by using the thermofield dynamics approach. Indeed, by considering temperature, we show that environmental states, while they become entangled with system, approach thermal coherent states with different phases. In addition, by considering the tunneling term, we study the interplay of the environmental cut-off frequency as well as the impacts of environmental temperature on the quantum speed limit in both cases, i.e., spin-boson system with and without tunneling term. In these studies, we indicate temperature play more important role in compare with cut-off frequency to control the quantumness of a spin system.

Thermal quantum gravity condensates in group field theory cosmology

The condensate cosmology programme of group field theory has produced several interesting results. The key idea is in the suggestion that a macroscopic homogeneous spacetime can be approximated by a dynamical condensate phase of the underlying microscopic system of an arbitrarily large number of candidate quanta of geometry. In this work, we extend the standard treatments in two ways: by using a class of thermal condensates, the coherent thermal states, which encode statistical fluctuations in quantum geometry; and, by introducing a suitable class of smearing functions as non-singular, well-behaved generalisations for relational clock frames in group field theory. In particular, we investigate an effective relational cosmological dynamics for homogeneous and isotropic spacetimes, extracted from a class of free group field theory models, and subsequently investigate aspects of its late and early times evolution. We find the correct classical limit of Friedmann equations at late times, with a bounce and accelerated expansion at early times. Specifically, we find additional correction terms in the evolution equations corresponding to the statistical contribution of the new thermal condensates in general; and, a higher upper bound on the number of e-folds, even without including any interactions.

Nonlinear thermal coherent states

Coherent states and their generalizations are normally appropriate candidates for describing radiation fields. Despite this, the effect of thermal noise on generalized coherent states has not been extensively studied. In fact, thermal effects are unavoidable at finite temperatures, and they should be taken into account to have a better agreement with experimental results. In this regard, we use the concept of thermal coherent states, which are indeed the standard coherent states including thermal effects. So, in this paper, by using a nonlinear coherent states approach, we generalize the thermal coherent states to their nonlinear counterparts. In other words, we find a natural link between the thermal coherent states and the nonlinear coherent states associated with nonlinear oscillator algebra. Afterwards, the nonclassicality features of the obtained states are numerically investigated to explore the roles of both nonlinearity and thermal noise in physical properties. The results show that the thermal effects lead to the transition from nonclassical states to classical ones. Moreover, it is seen that the operator-valued intensity-dependent function plays a leading role in controlling the depth as well as the domain of nonclassicality aspects.

Circuit complexity for generalized coherent states in thermal field dynamics

In this work, we study the circuit complexity for generalized coherent states in thermal systems by adopting the covariance matrix approach. We focus on the coherent thermal (CT) state, which is non-Gaussian and has a nonvanishing one-point function. We find that even though the CT state cannot be fully determined by the symmetric two-point function, the circuit complexity can still be computed in the framework of the covariance matrix formalism by properly enlarging the covariance matrix. Now the group generated by the unitary is the semiproduct of translation and the symplectic group. If the reference state is Gaussian, the optimal geodesic is still be generated by a horizontal generator such that the circuit complexity can be read from the generalized covariance matrix associated to the target state by taking the cost function to be $F_2$. For a single harmonic oscillator, we discuss carefully the complexity and its formation in the cases that the reference states are Gaussian and the target space is excited by a single mode or double modes. We show that the study can be extended to the free scalar field theory.

Density fluctuations and single-mode thermal states in the FRW universe

Using single-mode squeezed and coherent thermal states formalism, we analyzed the validity of the semiclassical Einstein equation (SCEE) in the flat Friedmann–Robertson–Walker universe by analyzing the density fluctuations in terms of a massive inflaton. In a single-mode squeezed thermal states the density fluctuations are too large; consequently, the semiclassical theory of gravity (SCTG) does not hold good, for squeezing parameter greater than unity, i.e., $$r_{s}>1$$; however, the theory is valid when this related squeezing parameter is smaller than the unity, i.e., $$r_{s}<<1$$ and $$r_{s}<1$$. Also, it is noted that the SCEE is dependable on coherent thermal state formalism. The current study provides a description of the density fluctuations as a result of the quantum and thermal effects in the SCTG.

Thermal representations in group field theory: squeezed vacua and quantum gravity condensates

We apply the formalism of thermofield dynamics to group field theory quantum gravity and construct thermal representations associated with generalised equilibrium Gibbs states using Bogoliubov transformations. The newly constructed class of thermal vacua are entangled, two-mode squeezed, thermofield double states. The corresponding finite temperature representations are inequivalent to the standard zero temperature one based on a degenerate vacuum. An interesting class of states, coherent thermal states, are defined and understood as thermal quantum gravity condensates.

Analysis and measurement of high-order photon correlations of light fields

&lt;sec&gt;High-order photon correlations of light fields are important for characterizing the quantum nature. Since Hanbury Brown and Twiss conducted the pioneering experiments in the 1950s, the HBT effect has inspired extensive research on high-order photon correlation in quantum optics, quantum information, and quantum imaging. The Single-photon counting module is one of the most widely used single-photon detectors. Due to its high detection efficiency and low dark counts in the visible and near-infrared region, it is reasonably chosen for basic research on quantum mechanics. Many researches have demonstrated that the maximum value of second-order photon correlation &lt;i&gt;g&lt;/i&gt;&lt;sup&gt;(2)&lt;/sup&gt;(&lt;i&gt;τ&lt;/i&gt;) at zero delay (&lt;i&gt;τ&lt;/i&gt; = 0) can be used to distinguish different light fields. Therefore, the HBT scheme containing two single photon detectors have been widely used in many advanced studies, such as space interference, ghost imaging, single photon detection with high efficiency, etc. However, higher-order photon correlations &lt;i&gt;g&lt;/i&gt;&lt;sup&gt;(&lt;i&gt;n&lt;/i&gt;)&lt;/sup&gt; (&lt;i&gt;n&lt;/i&gt; &gt; 2) can reveal more measurable characteristics of light fields, such as information about the non-Gaussian scattering process, the skewness and kurtosis of photon number distribution, etc. When the extended HBT scheme is used to measure higher-order photon correlations, the experimental conditions including quantum efficiency and background noise greatly affect the photon correlation measurement. The influences of the counting rate and resolution time of the detection system on the measurements are also very important and cannot be ignored. Therefore, the comprehensive considering of various influence factors is necessary for accurately measuring the high-order photon correlations and also a challenge.&lt;/sec&gt;&lt;sec&gt;In this paper, we present a method based on double Hanbury Brown-Twiss scheme for the accurate measuring of high-order photon correlations &lt;i&gt;g&lt;/i&gt;&lt;sup&gt;(&lt;i&gt;n&lt;/i&gt;)&lt;/sup&gt; (&lt;i&gt;n&lt;/i&gt; &gt; 2). The system consists of four single photon counting modules and is used to detect and analyze the joint distribution probability of temporal photon correlation. Considering the effects of the background noise and overall efficiency, theoretically, we analyze the correlations of the third- and fourth-order photon with the incident light intensity, squeezing parameter and photon number respectively for thermal state, coherent state, squeezed vacuum state, and Fock state. Meanwhile, experimentally we study the influences of resolution time and counting rate on correlations of the coherent state and thermal state with third- and fourth-order photon. On condition that the resolution time is 2&lt;sup&gt;10&lt;/sup&gt; ns and the counting rate is 80 kc/s, the correlations of third and fourth-order photon with the thermal state at zero time delay are accurately measured, and the relative statistical deviations of the measured vales from the theoretical values are 0.3% and 0.8%, respectively. In addition, the third- and fourth-order photon correlations of the thermal state at different delay times are also observed. It is demonstrated that the high-order photon correlations of light fields are measured accurately by comprehensively analyzing various influencing factors. This technique provides a promising and useful tool to investigate quantum correlated imaging and quantum coherence of light fields.&lt;/sec&gt;

A generative modeling approach for benchmarking and training shallow quantum circuits

Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications. Expanding the portfolio of such techniques, we propose a quantum circuit learning algorithm that can be used to assist the characterization of quantum devices and to train shallow circuits for generative tasks. The procedure leverages quantum hardware capabilities to its fullest extent by using native gates and their qubit connectivity. We demonstrate that our approach can learn an optimal preparation of the Greenberger-Horne-Zeilinger states, also known as “cat states”. We further demonstrate that our approach can efficiently prepare approximate representations of coherent thermal states, wave functions that encode Boltzmann probabilities in their amplitudes. Finally, complementing proposals to characterize the power or usefulness of near-term quantum devices, such as IBM’s quantum volume, we provide a new hardware-independent metric called the qBAS score. It is based on the performance yield in a specific sampling task on one of the canonical machine learning data sets known as Bars and Stripes. We show how entanglement is a key ingredient in encoding the patterns of this data set; an ideal benchmark for testing hardware starting at four qubits and up. We provide experimental results and evaluation of this metric to probe the trade off between several architectural circuit designs and circuit depths on an ion-trap quantum computer.

Holographic excited states in AdS black holes

We have recently presented a geometry dual to a Schwinger-Keldysh closed time contour, with two equal β/2 length Euclidean sections, which can be thought of as dual to the Thermo Field Dynamics formulation of the boundary CFT. In this work we study non-perturbative holographic excitations of the thermal vacuum by turning on asymptotic Euclidean sources. In the large-N approximation the states are found to be thermal coherent states and we manage to compute its eigenvalues. We pay special attention to the high temperature regime where the manifold is built from pieces of Euclidean and Lorentzian black hole geometries. In this case, the real time segments of the Schwinger-Keldysh contour get connected by an Einstein-Rosen wormhole through the bulk, which we identify as the exterior of a single maximally extended black hole. The Thermal-AdS case is also considered but, the Lorentzian regions become disconnected, its results mostly follows from the zero temperature case.

Full Counting Statistics of Electrons through Interaction of the Single Quantum Dot System with the Optical Field.

In this paper, using the particle-number-resolved master equation, the properties of full counting statistics (FCS) are investigated for a single quantum dot (QD) system interacting with optical fields in the thermal state, Fock state, coherent state, and coherent state with random phase. In these diverse quantum states of optical fields, average tunneling currents have different step shoulder heights at a lower bias voltage with the same light intensity, and a staircase-shaped current can be induced unexpectedly in vacuum state optical field. The characteristics of the Fano factor and skewness in the coherent state differ from those in all of the other cases. For avalanche-like transport at a lower bias voltage, the mechanism is a dynamical channel blockade in a moderate electron–photon interaction regime. There is a pronounced negative differential conductance that results from tuning the phase of the coherent state optical field in a symmetric QD system.

Classicalization of quantum state of detector by amplification process

It has been shown that a macroscopic system being in a high-temperature thermal coherent state can be, in principle, driven into a non-classical state by coupling to a microscopic system. Therefore, thermal coherent states do not truly represent the classical limit of quantum description. Here, we study the classical limit of quantum state of a more relevant macroscopic system, namely the pointer of a detector, after the phase-preserving linear amplification process. In particular, we examine to what extent it is possible to find the corresponding amplified state in a superposition state, by coupling the pointer to a qubit system. We demonstrate quantitatively that the amplification process is able to produce the classical limit of quantum state of the pointer, offering a route for a classical state in a sense of not to be projected into a quantum superposition state.

Photon-Number-Resolved Measurement of an Exciton-Polariton Condensate.

We measure the full photon-number distribution emitted from a Bose condensate of microcavity exciton polaritons confined in a micropillar cavity. The statistics are acquired by means of a photon-number-resolving transition edge sensor. We directly observe that the photon-number distribution evolves with the nonresonant optical excitation power from geometric to quasi-Poissonian statistics, which is canonical for a transition from a thermal to a coherent state. Moreover, the photon-number distribution allows one to evaluate the higher-order photon correlations, shedding further light on the coherence formation and phase transition of the polariton condensate. The experimental data are analyzed in terms of thermal-coherent states, which gives direct access to the thermal and coherent fraction from the measured distributions. These results pave the way for a full understanding of the contribution of interactions in light-matter condensates in the coherence buildup at threshold.