Average Photon Number 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.

Monitoring the Energy of a Cavity by Observing the Emission of a Repeatedly Excited Qubit.

The number of excitations in a large quantum system (harmonic oscillator or qudit) can be measured in a quantum nondemolition manner using a dispersively coupled qubit. It typically requires a series of qubit pulses that encode various binary questions about the photon number. Recently, a method based on the fluorescence measurement of a qubit driven by a train of identical pulses was introduced to track the photon number in a cavity, hence simplifying its monitoring and raising interesting questions about the measurement backaction of this scheme. A first realization with superconducting circuits demonstrated how the average number of photons could be measured in this way. Here we present an experiment that reaches single-shot photocounting and number tracking owing to a cavity decay rate 4 orders of magnitude smaller than both the dispersive coupling rate and the qubit emission rate. An innovative notch filter and pogo-pin-based galvanic contact makes possible these seemingly incompatible features. The qubit dynamics under the pulse train is characterized. We observe quantum jumps by monitoring the photon number via the qubit fluorescence as photons leave the cavity one at a time. Additionally, we extract the measurement rate and induced dephasing rate and compare them to theoretical models. Our method could be applied to quantum error correction protocols on bosonic codes or qudits.

Photon number adaptive single-photon detection with time-walk passive compensation.

In long-distance laser time transfer, such as satellite-to-satellite and satellite-to-ground, the accuracy of flight time measurement for photon pulses is significantly compromised by the time walk phenomenon, stemming from variations of the incident photon numbers. In this paper, we propose a single-photon detection method, which is adaptive to the photon number, and passively compensates for the time walk effect. This method utilizes a fiber ring to divide an incident photon pulse into a series of photon pulse trains, with each pulse in the train separated by equal time intervals and subject to equal attenuation. The last detected photon pulse in the pulse train can always be attenuated to a single-photon level sufficient to render the time walk effect negligible. The experimental results demonstrate that the proposed method effectively mitigates the time walk effect across a range of average photon numbers, spanning from 1 to 100. It provides high-precision single-photon detection for laser time transfer in complex and variable environments.

Unconventional photon blockade via two-photon absorption

The unconventional photon blockade, which relies on the physical mechanism of quantum interference, is primarily investigated using a general master equation, where a weak nonlinearity must be presented in the system to achieve photon antibunching. In this study, we explore the unconventional photon blockade using an alternative master equation known as the two-photon absorption master equation, which is derived from the system and environment interaction via two-photon absorption. Specifically, we find that the unconventional photon blockade can be triggered in two-coupled cavities, where each cavity interacts with a two-photon absorption environment. Different from unconventional photon blockade via the general master equation, we show that the two-photon absorption acts as the weak nonlinearity, and this photon blockade corresponds to a large average photon number. To derive optimal conditions for achieving this blockade, we propose a non-Hermitian Hamiltonian method to describe the mode loss caused by the two-photon absorption. In addition, we highlight the distinctions between our proposal and other approaches for generating single-photon states based on two-photon absorption.

Schrödinger cats coupled with cavities losses: the effect of finite and structured reservoirs

We discuss the generation of a Schrödinger cat in a nanocavity created by the coupling of an electromagnetic mode with an exciton in a quantum dot considering the dispersive limit of the Jaynes–Cummings model. More than the generation itself, we focus on the effects of the environment over the bosonic state in the nanocavity, which has losses simulated by coupling with two different kinds of reservoirs. In the first case, the interaction of the system with a finite reservoir shows that fragments of different sizes of the reservoir deliver the same amount of information about the physical system in the dynamics of the birth and death of the Schrödinger cat. The second case considers a structured reservoir, whose spectral density varies significantly with frequency. This situation becomes relevant in solid-state devices where quantum channels are embedded, as memory effects generally cannot be neglected. Under these circumstances, it is observed that the dynamics can differ substantially from the Markovian, presenting oscillations related to the average number of photons. These oscillations influence the information flow between the system and the environment, evidenced here by the measurement of non-Markovianity.

Quantum tricriticality in a generalized quantum Rabi system

Quantum tricriticality, a unique form of high-order criticality, is expected to exhibit fascinating features including unconventional critical exponents and universal scaling laws. However, a quantum tricritical point (QTCP) is much harder to access, and the corresponding phenomena at tricriticality have rarely been investigated. In this study, we explore a tricritical quantum Rabi model, which incorporates a non-trivial parameter to adjust the coupling ratio between a cavity and a three-level atom. The QTCP emerges at the intersection of first- and second-order superradiant phase transitions according to Landau theory. By using finite-frequency scaling analysis on quantum fluctuations and the average photon number, universal critical exponents differentiate the QTCP from the second-order critical point. Our results indicate that the phase transition at the tricritical point goes beyond the conventional second-order phase transition. Our work explores an interesting direction in the generalization of the well-known Rabi model for the study of higher-order critical points due to its high control and tunability.

Effects of classical drivings on the power broadening of atomic lineshapes

In the framework of the Jaynes–Cummings model, we investigate how atomic lineshapes are affected by coherently driving the atom–field interaction. We pay particular attention to the two-level atom interaction with a thermal cavity field when both are influenced by external classical fields. Adopting a density matrix formalism, we calculate the average atomic inversion and demonstrate how the corresponding lineshapes vary as a function of the average number of thermal photons and the atom–field classical coupling. Furthermore, we compare these results with those obtained from the standard Jaynes–Cummings model and validate our findings through numerical calculations.

First-order quantum phase transition in the two-qubit squeezed Rabi model

We study the ground state of the two-qubit squeezed Rabi model. Two special transformations are found to diagonalize the system Hamiltonian when each qubit’s frequency is close to the field frequency, where both the squeezing and counterrotating-wave interactions are removed, leading to an effective integrable Hamiltonian. The analytical ground state is determined and matches with numerical solutions well for a range of squeezing strengths and qubit-field detunings in the ultrastrong-coupling regime. We demonstrate that the ground state exhibits a first-order quantum phase transition at a phase boundary linearly induced by the squeezed light. We characterize the two-qubit negativity analytically and find that its two-qubit entanglement increases with the increasing squeezing strength nonlinearly. The average photon numbers of the field mode and variances of position and momentum quadratures are also analyzed and discovered to have a nonlinear relation with the squeezing strength. Finally, we discuss the experimental scheme and realization possibility of the predicted results.

Far-field superresolution of thermal sources by double homodyne or double array homodyne detection

We propose two schemes for estimating the separation of two thermal sources via double homodyne and double array homodyne detection considering the joint measurement of conjugate quadratures of the image plane field.By using the Cramér–Rao bound, we demonstrate that the two schemes can estimate the separation well below the Rayleigh limit and have an advantage over direct imaging when the average photon number per source exceeds five.For arbitrary source strengths, double homodyne detection is superior to homodyne detection when the separation is above 25/4σ/N s , σ is the beam width, N s is the average photon number per source.A larger separation can be estimated better via double array homodyne detection with the superiority of flexible operation compared with other schemes. High-speed and high-efficiency detection enables the measurement schemes with potential practical applications in fluorescence microscopy, astronomy and quantum imaging.

Measurement of Small Photon Numbers in Circuit QED Resonators.

Off-resonant interaction of fluctuating photons in a resonator with a qubit increases the qubit dephasing rate. We use this effect to measure a small average number of intracavity photons that are coherently or thermally driven. For spectral resolution, we do this by subjecting the qubit to a Carr-Purcell-Meiboom-Gill sequence and record the qubit dephasing rate for various periods between qubit π pulses. The recorded data is then analyzed with formulas for the photon-induced dephasing rate derived for the non-Gaussian noise regime with an arbitrary ratio of the resonator dispersive shift to decay rate. We show that the presented Carr-Purcell-Meiboom-Gill dephasing rate formulas agree well with experimental results and demonstrate measurement of thermal and coherent photon populations at the level of a few 10^{-4}.

Dynamics of entangled Greenberger — Horne — Zeilinger states in three qubits thermal Tavis — Cummings model

In this paper, we investigated the dynamics of systems of two and three identical qubits interacting resonantly with a selected mode of a thermal field of a lossless resonator. We found solutions of the quantum time-dependent Liouville equation for various three- and two-qubit entangled states of qubits. Based on these solutions, we calculated the criterion of the qubit entanglement — fidelity. The results of numerical calculations of the fidelity showed that increasing the average number of photons in a mode leads to a decrease in the maximum degree of entanglement. It is shown that the two-qubit entangled state is more stable with respect to external noise than the three-qubit entangled Greenberger — Horne — Zeilinger states (GHZ). Moreover, a genuine entangled GHZ-state is more stable to noise than a GHZ-like entangled state.

Quench dynamics in the Jaynes-Cummings-Hubbard and Dicke models

Both the Jaynes-Cummings-Hubbard (JCH) and Dicke models can be thought of as idealised models of a quantum battery. In this paper we numerically investigate the charging properties of both of these models. The two models differ in how the two-level systems are contained in cavities. In the Dicke model, the N two-level systems are contained in a single cavity, while in the JCH model the two-level systems each have their own cavity and are able to pass photons between them. In each of these models we consider a scenario where the two-level systems start in the ground state and the coupling parameter between the photon and the two-level systems is quenched. Each of these models display a maximum charging power that scales with the size of the battery N and no super charging was found. Charging power also scales with the square root of the average number of photons per two-level system m for both models. Finally, in the JCH model, the power was found to charge inversely with the photon-cavity coupling κ.

Dissipation-Induced Photon Blockade in the Anti-Jaynes–Cummings Model

Due to the fundamental differences between the quantum world and the classical world, some phenomena, such as entanglement and wave–particle duality, only exist in the quantum realm. These peculiar phenomena cannot be demonstrated by classical means: Quantum networks, quantum cryptography, and quantum precision measurements all require quantum sources. Photons are particularly well-suited as quantum sources owing to their minimal interaction with the environment, high flight speed, and ease of interaction with current typical quantum systems. Single-photon sources include pulsed excitation of quantum dots, spontaneous parametric down-conversion, and photon blockade. Herein, we propose that the anti-Jaynes–Cummings model can induce a pronounced photon antibunching effect when subjected to intense cavity dissipation. Similar to the photon blockade caused by strong photon–photon interaction, this antibunching effect is referred to as ’dissipation-induced blockade’. Our findings indicate that the minimum decay rate of a qubit, coupled with a high decay rate for photons, is conducive to achieving strong antibunching within the system. Notably, g(2)(0)<g(2)(τ), a characteristic of photon antibunching, is only valid under the optimal condition Δ=0. Conversely, g(2)(0)<1 is satisfied across all parameters, indicating that g(2)(0)<1 is not a prerequisite for antibunching in the anti-Jaynes–Cummings model. Moreover, under the optimal conditions of the antibunching effect, the average photon number attains its peak value. Consequently, the current anti-Jaynes–Cummings model is promising for developing single-photon sources characterized by excellent purity and average photon number.

Taming the Rotating Wave Approximation

The interaction between light and matter is one of the oldest research areas of quantum mechanics, and a field that just keeps on delivering new insights and applications. With the arrival of cavity and circuit quantum electrodynamics we can now achieve strong light-matter couplings which form the basis of most implementations of quantum technology. But quantum information processing also has high demands requiring total error rates of fractions of percentage in order to be scalable (fault-tolerant) to useful applications. Since errors can also arise from modelling, this has brought into center stage one of the key approximations of quantum theory, the Rotating Wave Approximation (RWA) of the quantum Rabi model, leading to the Jaynes-Cummings Hamiltonian. While the RWA is often very good and incredibly useful to understand light-matter interactions, there is also growing experimental evidence of regimes where it is a bad approximation. Here, we ask and answer a harder question: for which experimental parameters is the RWA, although perhaps qualitatively adequate, already not good enough to match the demands of scalable quantum technology? For example, when is the error at least, and when at most, 1%? To answer this, we develop rigorous non-perturbative bounds taming the RWA. We find that these bounds not only depend, as expected, on the ratio of the coupling strength and the oscillator frequency, but also on the average number of photons in the initial state. This confirms recent experiments on photon-dressed Bloch-Siegert shifts. We argue that with experiments reporting controllable cavity states with hundreds of photons and with quantum error correcting codes exploring more and more of Fock space, this state-dependency of the RWA is increasingly relevant for the field of quantum computation, and our results pave the way towards a better understanding of those experiments.

Quantitative probability estimation of light-induced inactivation of SARS-CoV-2

During the COVID pandemic caused by the SARS-CoV-2 virus, studies have shown the efficiency of deactivating this virus via ultraviolet light. The damage mechanism is well understood: UV light disturbs the integrity of the RNA chain at those locations where specific nucleotide neighbors occur. In this contribution, we present a model to address certain gaps in the description of the interaction between UV photons and the RNA sequence for virus inactivation. We begin by exploiting the available information on the pathogen’s morphology, physical, and genomic characteristics, enabling us to estimate the average number of UV photons required to photochemically damage the virus’s RNA. To generalize our results, we have numerically generated random RNA sequences and checked that the distribution of pairs of nucleotides susceptible of damage for the SARS-CoV-2 is within the expected values for a random-generated RNA chain. After determining the average number of photons reaching the RNA for a preset level of fluence (or photon density), we applied the binomial probability distribution to evaluate the damage of nucleotide pairs in the RNA chain due to UV radiation. Our results describe this interaction in terms of the probability of damaging a single pair of nucleotides, and the number of available photons. The cumulative probability exhibits a steep sigmoidal shape, implying that a relatively small change in the number of affected pairs may trigger the inactivation of the virus. Our light-RNA interaction model quantitatively describes how the fraction of affected pairs of nucleotides in the RNA sequence depends on the probability of damaging a single pair and the number of photons impinging on it. A better understanding of the underlying inactivation mechanism would help in the design of optimum experiments and UV sanitization methods. Although this paper focuses on SARS-CoV-2, these results can be adapted for any other type of pathogen susceptible of UV damage.

Witnessing edge modes in trimerized circuit quantum electrodynamic lattice

We propose a scheme to investigate and witness edge modes of general one-dimensional photonic trimers in a circuit quantum electrodynamic lattice. These in-gap edge modes are strictly and analytically solved and the criteria for their emergence are indicated respectively. Moreover, the energy spectrum of the system shows two different regimes characterized by a discrepancy in the number of edge modes. Specifically, while there are always a couple of edge modes only present at one single boundary in both the regimes, one of the regimes also shows another pair of edge modes localized on the opposite boundary. Furthermore, these edge modes are witnessed with the aid of continuous-time quantum walks and average photon number measurements. Our scheme provides a comprehensive method for studying the edge modes of matter.

Threshold studies for a hot beam superradiant laser including an atomic guiding potential

Motivated by the outstanding short time stability and reliable continuous operation properties of microwave clock masers, intense worldwide efforts target the first implementation of their optical analogues based on narrow optical clock transitions and using laser cooled dilute atomic gases. While as a central line of research large efforts are devoted to create a suitably dense continuous ultracold and optically inverted atom beam source, recent theoretical predictions hint at an alternative implementation using a filtered thermal beam at much higher density. Corresponding numerical studies give encouraging results but the required very high densities are sensitive to beam collimation errors and inhomogeneous shifts. Here we present extensive numerical studies of threshold conditions and the predicted output power of such a superradiant laser involving realistic particle numbers and velocities along the cavity axis. Detailed studies target the threshold scaling as a function of temperature as well as the influence of eliminating the hottest part of the atomic distribution via velocity filtering and the benefits of additional atomic beam guiding. Using a cumulant expansion approach allows us to quantify the significance of atom-atom and atom-field correlations in such configurations. We predict necessary conditions to achieve a certain threshold photon number depending on the atomic temperature and density. In particular, we show that the temperature threshold can be significantly increased by using more atoms. Interestingly, a velocity filter removing very fast atoms has only almost negligible influence despite their phase perturbing properties. On the positive side an additional conservative optical guiding towards cavity mode antinodes leads to significantly lower threshold and higher average photon number. Interestingly we see that higher order atom-field and direct atom-atom quantum correlations play only a minor role in the laser dynamics, which is a bit surprising in the superradiant regime.

Broadband Spectroscopy and Interferometry with Undetected Photons at Strong Parametric Amplification

AbstractNonlinear interferometry with entangled photons allows for characterizing a sample without detecting the photons interacting with it. This method enables highly sensitive optical sensing in the wavelength regions where efficient detectors are still under development. Recently, nonlinear interferometry has been applied to interferometric measurement techniques with broadband light sources, such as Fourier‐transform infrared spectroscopy and infrared optical coherence tomography. However, they have been demonstrated with photon pairs produced through spontaneous parametric down‐conversion (SPDC) at a low parametric gain, where the average number of photons per mode is much smaller than one. The regime of high‐gain SPDC offers several important advantages, such as the amplification of light after its interaction with the sample and a large number of photons per mode at the interferometer output. This work presents broadband spectroscopy and high‐resolution optical coherence tomography with undetected photons generated via high‐gain SPDC in an aperiodically poled lithium niobate crystal. To prove the principle, reflective Fourier‐transform near‐infrared spectroscopy with a spectral bandwidth of 17 THz and optical coherence tomography with an axial resolution of 11 µm are demonstrated.

Geometric versus Entropic Gaussian Correlations in an Open Quantum System of Two Bosonic Modes

Different types of geometric and entropic quantum correlation quantifiers are studied for a system composed of two resonant bosonic modes embedded in a thermal bath. The description of the evolution of the correlation measures is formulated in the framework of the theory of open systems, based on completely positive quantum dynamical semigroups, by using both a geometric and entropic quantification of total nonclassical correlations of Gaussian states. We consider the special case when the initial squeezed thermal state of the system preserves its form in time. We show that time evolution of the measures strongly depends on the parameters characterising the initial state of the system (squeezing parameter and average thermal photon numbers of the two modes) and of the thermal environment (temperature of the thermal bath and dissipation rate). In the limit of large times all the considered measures asymptotically tend to zero value, corresponding to an asymptotic bimodal uncorrelated product state. We make a comparison between the behaviour of the evolution in time of the Gaussian geometric quantum correlations and Gaussian entropic quantum correlations.

Thermodynamics of the Ramsey Zone.

We studied the thermodynamic properties such as the entropy, heat (JQ), and work (JW) rates involved when an atom passes through a Ramsey zone, which consists of a mode field inside a low-quality factor cavity that behaves classically, promoting rotations on the atomic state. Focusing on the atom, we show that JW predominates when the atomic rotations are successful, maintaining its maximum purity as computed by the von Neumann entropy. Conversely, JQ stands out when the atomic state ceases to be pure due to its entanglement with the cavity mode. With this, we interpret the quantum-to-classical transition in light of the heat and work rates. Besides, we show that, for the cavity mode to work as a Ramsey zone (classical field), several photons (of the order of 106) need to cross the cavity, which explains its classical behavior, even when the inside average number of photons is of the order of unity.