We have recently put forth several schemes of unconventional, nonlinearly-enabled thermodynamic (TD) devices that can operate in either the classical or the quantum domain by transforming thermal-state input in multiple uncorrelated modes into non-gaussian state output in selected modes: a four-mode Kerr-nonlinear interferometer that acts as a heat engine; two coupled Kerr-nonlinear Mach-Zehnder interferometers that act as a phase microscope with unprecedented phase resolution; and a noise sensor that can distinguish between unknown nonlinear quantum processes. These schemes reveal the unique merits of nonlinear TD devices: their ability to act in an autonomous, fully coherent, dissipationless fashion, unlike their conventional counterparts. Here we present the opportunities and challenges facing this new paradigm of nonlinear (NL) quantum and classical TD devices along the following lines: (A) Linear versus nonlinear multimode transformations in TD devices: what are the principal distinctions between the two types of transformations? (B) Classical versus quantum effects in NL TD devices: what are their main differences? Is quantumness an advantage or a disadvantage? (C) Deterministic methods of achieving giant nonlinearity at the few-photon level via coherent processes, including multiatom-bath interactions which can paradoxically yield NL Hamiltonian effects: their comparison with probabilistic, measurement-based methods that can achieve similar NL effects in the quantum domain.

We have recently shown that interferometers with nonlinear cross-Kerr coupling allow us to coherently filter incident thermal noise, transforming it into an information resource. State-of-the-art technology enables Kerr-nonlinear interferometers to achieve supersensitive resolution in noise sensors or microscopes using thermal noise sources of few photons.

We put forth the concept of quantum noise sensing in nonlinear two-mode interferometers coupled to mechanical oscillators. These autonomous machines are capable of sensing quantum nonlinear correlations of two-mode noisy fields via their thermodynamic variable of extractable work, alias work capacity (WC) or ergotropy. The fields are formed by thermal noise input via its interaction with multi-level systems inside the interferometer. Such interactions amount to the generation of two-mode quantum nonlinear gauge fields that may be partly unknown. We show that by monitoring a mechanical oscillator coupled to the interferometer, one can sense the WC of one of the output field modes and thereby reveal the quantum nonlinear correlations of the field. The proposed quantum sensing method can provide an alternative to quantum multiport interferometry where the output field is unraveled by tomography. This method may advance the simulation and control of multimode quantum nonlinear gauge fields.

Estimation of the phase delay between interferometer arms is the core of transmission phase microscopy. Such phase estimation may exhibit an error below the standard quantum (shot-noise) limit, if the input is an entangled two-mode state, e.g., a N00N state. We show, by contrast, that such supersensitive phase estimation (SSPE) is achievable by incoherent, e.g., thermal, light that is injected into a Mach-Zehnder interferometer via a Kerr-nonlinear two-mode coupler. Phase error is shown to be reduced below 1/n¯, n¯ being the mean photon number, by thermal input in such interferometric setups, even for small nonlinear phase shifts per photon pair or for significant photon loss. Remarkably, the phase accuracy achievable in such setups by thermal input surpasses that of coherent light with the same n¯. Available mode couplers with giant Kerr nonlinearity that stem either from dipole-dipole interactions of Rydberg polaritons in a cold atomic gas, or from cavity-enhanced dispersive atom-field interactions, may exploit such effects to substantially advance interferometric phase microscopy using incoherent, faint light sources.

We provide a MATLAB numerical guide at the beginner level to support students starting their research careers in theoretical quantum optics and related areas. These resources are also valuable for undergraduate and graduate students working on semester projects in similar fields.

We propose heat machines that are nonlinear, coherent, and closed systems composed of few field (oscillator) modes. Their thermal-state input is transformed by nonlinear Kerr interactions into nonthermal (non-Gaussian) output with controlled quantum fluctuations and the capacity to deliver work in a chosen mode. These machines can provide an output with strongly reduced phase and amplitude uncertainty that may be useful for sensing or communications in the quantum domain. They are experimentally realizable in optomechanical cavities where photonic and phononic modes are coupled by a Josephson qubit or in cold gases where interactions between photons are transformed into dipole-dipole interacting Rydberg atom polaritons. This proposed approach is a step toward the bridging of quantum and classical coherent and thermodynamic descriptions.

Effects of non-ideal optical components in realizing quantum Zeno effect in an all-optical setup are analyzed. Beam splitters are the important components in this experimental configuration. Non-uniform transmission coefficient, photon absorption and thermal noise are considered. Numerical simulation of the experiment is performed using the Monte Carlo wavefunction method. It is argued that there is an optimal number of beam splitters to be used for maximizing the expected output in the experiment.

The processing of information and computation is undergoing a paradigmatic shift since the realization of the enormous potential of quantum features to perform these tasks. Coupled cavity array is one of the well-studied systems to carry out these tasks. It is a versatile platform for quantum networks for distributed information processing and communication. Cavities have the salient feature of retaining photons for longer durations, thereby enabling them to travel coherently through the array without losing them in dissipation. Many quantum information protocols have been implemented in arrays of coupled cavities. These advancements promise the suitability of cavity arrays for large-scale quantum communications and computations. This article reviews a few theoretical proposals and experimental realizations of quantum information tasks in cavities.

An experimental scheme for the measurement of entanglement between two two-level atoms is proposed. This scheme requires one of the two entangled atoms to interact with a cavity field dispersively, and it is shown that by measuring the zero time-delay second-order coherence function of the cavity field, one can measure the concurrence of an arbitrary Bell-like atomic two-qubit state. As this scheme requires only one of the atoms to interact with the measured cavity, the entanglement quantification becomes independent of the location of the other atom. Therefore, this scheme can have important implications for entanglement quantification in distributed quantum systems.

The measurement of the position-momentum Einstein-Podolsky-Rosen (EPR) correlations of a two-photon state is important for many quantum information applications ranging from quantum key distribution to coincidence imaging. However, all the existing techniques for measuring the position-momentum EPR correlations involve coincidence detection and thus suffer from issues that result in less accurate measurements. In this article, we propose and demonstrate an experimental scheme that does not require coincidence detection for measuring the EPR correlations. Our technique works for two-photon states that are pure, irrespective of whether the state is separable or entangled. We theoretically show that if the pure two-photon state satisfies a certain set of conditions then the position-momentum EPR correlations can be obtained by doing the intensity measurements on only one of the photons. We experimentally demonstrate this technique for pure two-photon states produced by type-I spontaneous parametric down-conversion, and to the best of our knowledge, we report the most accurate experimental measurement of position-momentum EPR correlations.

Using the zero time-delay second-order correlation function for studying photon statistics, we investigate how the photon statistics of field-modes generated by the parametric down-conversion (PDC) process depends on the photon statistics of the pump field-mode. We derive general expressions for the zero time-delay second-order correlation function of the down-converted field-modes for both multi-mode and single-mode PDC processes. We further study these expressions in the weak down-conversion limit. We show that for a two-photon two-mode PDC process, in which a pump photon splits into two photons into two separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to twice that of the pump field-mode. Furthermore, for an n-photon n-mode down-conversion process, in which a pump photon splits into n photons into n separate field-modes, the zero time-delay second-order correlation function of the individual down-converted field-modes is equal to 2(n−1) times that of the pump field- mode. However, in contrast to multimode PDC processes, for a single-mode PDC process, in which a pump photon splits into two or more photons into a single mode, the zero time-delay second-order correlation function of the down-converted field-mode is not proportional to that of the pump in the weak down-conversion limit. Nevertheless, we find it to be inversely proportional to the average number of photons in the pump field-mode.

Controlled heat transfer and thermal rectification in a system of two coupled cavities connected to thermal reservoirs are discussed. Embedding a dispersively interacting two-level atom in one of the cavities allows switching from a thermally conducting to resisting behavior. By properly tuning the atomic state and system–reservoir parameters—in particular, system–reservoir couplings and resonance frequencies—the direction of the current can be reversed. It is shown that a large thermal rectification is achievable in this system by tuning the cavity–reservoir and cavity–atom couplings. Partial recovery of diffusive heat transport in an array of N cavities containing one dispersively coupled atom is discussed.

We study transfer of single photon in an one-dimensional finite Glauber-Fock cavity array whose coupling strengths satisfy a square root law. The evolved state in the array can be mapped to an upper truncated coherent state if the cavities are resonant. Appropriate choices of resonance frequencies provide perfect transfer of a photon between any two cavities in the array. Perfect transfer of the photon allows perfect quantum state transfer between the cavities. Our findings may help in realizing quantum communication and information processing in photonic lattices.

Number state filtered coherent states are a class of nonclassical states obtained by removing one or more number states from a coherent state. Phase sensitivity of an interferometer is enhanced if these nonclassical states are used as input states. The optimal phase sensitivity, which is related to the quantum Cramer–Rao bound for the input state, improves beyond the standard quantum limit. It is argued that the removal of more than one suitable number state leads to better phase sensitivity. As an important limiting case in this context, the even and odd coherent states, where the odd and even number states are filtered from coherent state, respectively, are considered. The optimal phase sensitivity for these limiting cases equals that of the squeezed vacuum. It is observed that the improvement in phase sensitivity is not in direct proportion to the nonclassicality of the input states.

Quantum dense coding is a protocol for transmitting two classical bits of information from a sender (Alice) to a remote receiver (Bob) by sending only one quantum bit (qubit). In this article, we propose an experimentally feasible scheme to realize quantum dense coding via entanglement swapping in a cavity array containing a certain number of two-level atoms. Proper choice of system parameters such as atom-cavity and inter-cavity couplings allows perfect transfer of information. A high fidelity transfer of information is shown to be possible by using recently achieved experimental values in the context of photonic crystal cavities and superconducting resonators. To mimic experimental imperfections, disorder in both the coupling strengths and resonance frequencies is considered.

Recently, a basis-invariant measure of coherence known as the intrinsic degree of coherence has been established for classical and single-particle quantum states [J. Opt. Soc. Am. B 36, 2765 (2019)]. In this article, we use the same mathematical construction to define the intrinsic degree of coherence of two-qubit states and demonstrate its usefulness in quantifying two-particle quantum correlations and entanglement. In this context, we first show that the intrinsic degree of coherence of a two-qubit state puts an upper bound on the violations of Bell inequalities that can be achieved with the state and that a two-qubit state with an intrinsic degree of coherence less than 1/√3 cannot violate Bell inequalities. We then show that the quantum discord of a two-qubit state, which quantifies the amount of quantum correlations available in the two-qubit state for certain tasks, is bounded from above by the intrinsic degree of coherence of the state. Next, in the context of two-particle entanglement, we show that the range of values that the concurrence of a two-qubit state can take is decided by the intrinsic degree of coherence of the two-qubit state together with that of the individual qubits. Finally, for the polarization two-qubit states generated by the parametric down-conversion of a pump photon, we propose an experimental scheme to measure the intrinsic degree of coherence of two-qubit states. We also present our theoretical study that shows how the intrinsic degree of coherence of a pump photon dictates the maximum intrinsic degree of coherence of the generated two-qubit state.

Spontaneous parametric down-conversion (SPDC) is the most widely used process for generating photon pairs entangled in various degrees of freedom such as polarization, time-energy, position-transverse momentum, and angle-orbital angular momentum (OAM). In SPDC, a pump photon interacts with a non-linear optical crystal and splits into two entangled photons called the signal and the idler photons. The SPDC process has been studied extensively in the last few decades for various pump and crystal configurations, and the entangled photon pairs produced by SPDC have been used in numerous experimental studies on quantum entanglement and entanglement-based real-world quantum-information applications. In this tutorial article, we present a thorough study of phase matching in BBO crystals for spontaneous parametric down-conversion and thereby also investigate the generation of entangled photons in such crystals. First, we present a theoretical derivation of two-photon wavefunction produced by SPDC in the frequency and transverse momentum bases. We then discuss in detail the effects due to various crystal and pump parameters including the length of the crystal, the angle between the optic axis and the pump propagation direction, the pump incidence angle on the crystal surface, the refraction at the crystal surfaces, and the pump propagation direction inside the crystal. These effects are extremely relevant in experimental situations. We then present our numerical and experimental results in order to illustrate how various experimental parameters affect the phase matching and thus the generation of entangled photons. Finally, using the two-photon wavefunction in the transverse wave-vector basis, we show how to derive the two-photon wavefunction in the OAM basis and thereby calculate the two-photon angular Schmidt spectrum. We expect this article to be useful for researchers working in various capacities with entangled photons generated by SPDC in BBO crystals.

Using the zero time-delay second-order correlation function, we investigate how the photon statistics of the field-modes generated by parametric down-conversion (PDC) process depends on photon statistics of the pump field-mode.

We propose a scheme to implement quantum controlled NOT gate and quantum phase gate in an optomechanical system based on phonon blockade. For appropriate choices of system parameters, the fidelities of both quantum gate operations are very close to unity in the absence of dissipation. Using recently achieved experimental values in a mechanical resonator coupled to a microwave cavity, we show that the quantum gate can be realized experimentally with very high fidelity.

Number state filtering in coherent states leads to sub-Poissonian photon statistics. These states are more suitable for phase estimation when compared with the coherent states. Nonclassicality of these states is quantified in terms of the negativity of the Wigner function and the entanglement potential. Filtering of the vacuum from a coherent state is almost like the photon addition. However, filtering makes the state more resilient against dissipation than photon addition. Vacuum state filtered coherent states perform better than the photon-added coherent states for a two-way quantum key distribution protocol. A scheme to generate these states in multi-photon atom–field interaction is presented.

A system of two coupled cavities with N - 1 photons is shown to be dynamically equivalent to an array of N coupled cavities containing one photon. Every transition in the two cavity system has a dual phenomenon in terms of photon transport in the cavity array. This duality is employed to arrive at the required coupling strengths and nonlinearities in the cavity array so that controlled photon transfer is possible between any two cavities. This transfer of photons between two of the cavities in the array is effected without populating the other cavities. The condition for perfect transport enables perfect state transfer between any two cavities in the array. Further, possibility of high fidelity generation of generalized NOON states in two coupled cavities, which are dual to the Bell states of the photon in the cavity array, is established.

We study photon localization and delocalization in a system of two nonlinear cavities with intensity-dependent coupling. These two features are analogous to the bunching and antibunching of photons. It is shown that complete localization or delocalization is possible for proper choices of the strengths of nonlinearity, inter-cavity detuning, and inter-cavity coupling. The role of the relative phase in the initial superposition in attaining localization and delocalization is discussed. Effects of dissipation and decoherence are considered, and the role of quantum interference in mitigating these effects is explored.

Localization and delocalization of two photons in an array of cavities are examined. Role of entanglement and relative phase of the initial state in the occurrence of localization or delocalization during time evolution is elucidated.