Photon-photon Correlations Research Articles

Temporal coherences of atomic chaotic light sources: The Siegert relation and its generalisation to higher-order correlation functions

Light is characterized by its electric field, yet quantum optics has revealed the importance of monitoring photon-photon correlations at all orders. We here present a comparative study of two experimental setups, composed of cold and warm rubidium atoms, respectively, which allow us to probe and compare photon correlations. The former operates in the quantum regime where spontaneous emission dominates, whereas the latter exhibits a temperature-limited coherence time. We demonstrate our capability to measure photon correlations up to the fourth order which could be useful to better characterize light scattered by cold atoms beyond the chaotic statistics.

First-order optical coherence of photonic-dimer coherent states.

Photon-photon correlations assume a pivotal significance in optical coherence. Recently, a new, to the best of our knowledge, type of quantum photonic states, the coherent state of photonic dimers, has been introduced, wherein the fundamental building blocks are two-photon bound states, instead of individual photons as in conventional lasers. In this Letter, we investigate the first-order coherence properties of the photonic-dimer coherent states, as well as the interference patterns in a double-slit interferometer setup, and compare with the coherence properties of other optical light sources, e.g., the conventional laser and the thermal light.

Quantifying Förster Resonance Energy Transfer from Single Perovskite Quantum Dots to Organic Dyes.

Colloidal quantum dots (QDs) are promising regenerable photoredox catalysts offering broadly tunable redox potentials along with high absorption coefficients. QDs have thus far been examined for various organic transformations, water splitting, and CO2 reduction. Vast opportunities emerge from coupling QDs with other homogeneous catalysts, such as transition metal complexes or organic dyes, into hybrid nanoassemblies exploiting energy transfer (ET), leveraging a large absorption cross-section of QDs and long-lived triplet states of cocatalysts. However, a thorough understanding and further engineering of the complex operational mechanisms of hybrid nanoassemblies require simultaneously controlling the surface chemistry of the QDs and probing dynamics at sufficient spatiotemporal resolution. Here, we probe the ET from single lead halide perovskite QDs, capped by alkylphospholipid ligands, to organic dye molecules employing single-particle photoluminescence spectroscopy with single-photon resolution. We identify a Förster-type ET by spatial, temporal, and photon-photon correlations in the QD and dye emission. Discrete quenching steps in the acceptor emission reveal stochastic photobleaching events of individual organic dyes, allowing a precise quantification of the transfer efficiency, which is >70% for QD-dye complexes with strong donor-acceptor spectral overlap. Our work explores the processes occurring at the QD/molecule interface and demonstrates the feasibility of sensitizing organic photocatalysts with QDs.

Photon-photon correlations in Ag+Ag collisions at √SNN = 2.55 GeV

Abstract. Photons, as penetrative probes, can deliver information about early stages of heavy-ion collisions, in contrast to hadrons, whose kinematics are determined after the freeze-out era. Given that, they provide access to quantities inaccessible for many other particle species. However, due to technical challenges of photon detection and dominance of photons from particle decays, exploiting their properties requires significant effort. Femtoscopy, a technique used to investigate the space-time characteristics of the source area, is sensitive to the emission sequence of studied particles. Hence, it can be utilized as a tool to separate photons originating from different sources. Studying femto-scopic correlations of photons can offer a new and unique perspective on source parameters before kinematic freeze-out. Using data from Ag+Ag collisions at √SNN = 2.55 GeV, collected by the HADES spectrometer, a preliminary study of photon-photon correlations was performed.

Phonon Signatures in Photon Correlations.

We show that the second-order, two-time correlation functions for phonons and photons emitted from a vibronic molecule in a thermal bath result in bunching and antibunching (a purely quantum effect), respectively. Signatures relating to phonon exchange with the environment are revealed in photon-photon correlations. We demonstrate that cross-correlation functions have a strong dependence on the order of detection giving insight into how phonon dynamics influences the emission of light. This work offers new opportunities to investigate quantum effects in condensed-phase molecular systems.

Imaging via Correlation of X-Ray Fluorescence Photons.

We demonstrate that x-ray fluorescence emission, which cannot maintain a stationary interference pattern, can be used to obtain images of structures by recording photon-photon correlations in the manner of the stellar intensity interferometry of Hanbury Brown and Twiss. This is achieved utilizing femtosecond-duration pulses of a hard x-ray free-electron laser to generate the emission in exposures comparable to the coherence time of the fluorescence. Iterative phasing of the photon correlation map generated a model-free real-space image of the structure of the emitters. Since fluorescence can dominate coherent scattering, this may enable imaging uncrystallised macromolecules.

Waveguide quantum electrodynamics: Collective radiance and photon-photon correlations

Quantum emitters coupled to waveguides experience long-range interactions mediated by photons. This leads to superradiant and subradiant states, photon bound states, and various mechanisms for the preparation of entangled states of the emitters. This article reviews experiments on a wide range of systems and their description by theoretical methods and insights from different fields of physics.

Photon-photon correlations from a pair of strongly coupled two-level emitters

We investigate two-color photon correlations in the light emitted by two strongly driven, strongly interacting two-level emitters. The correlations are interpreted introducing the collective dressed states picture, which allows us to describe both bunching and antibunching based on the allowed and prohibited transitions. At odds from weakly interacting emitters, the strong interaction lifts the degeneracy of the energy differences between the different states, leading to a temporal breaking of symmetry for the correlations: photons of different frequencies may not be emitted in any order. Finally, we show that most of the virtual processes, which involve pairs of photons, yield nonclassical correlations when the sum of their energies fits any of the interaction-induced sidebands in the emitted spectrum. In particular, depending on the frequency of the emitted photons, correlations strong enough to violate Bell inequalities can appear.

Quantum Borrmann effect for dissipation-immune photon-photon correlations

We study theoretically the second-order correlation function $g^{(2)}(t)$ for photons transmitted through a periodic Bragg-spaced array of superconducting qubits, coupled to a waveguide. We demonstrate that photon bunching and anti-bunching persist much longer than both radiative and non-radiative lifetimes of a single qubit. The photon-photon correlations become immune to non-radiative dissipation due to the Borrmann effect, that is a strongly non-Markovian collective feature of light-qubit coupling inherent to the Bragg regime. This persistence of quantum correlations opens new avenues for enhancing the performance of setups of waveguide quantum electrodynamics.

Inelastic Scattering of Photon Pairs in Qubit Arrays with Subradiant States.

We develop a rigorous theoretical approach for analyzing inelastic scattering of photon pairs in arrays of two-level qubits embedded into a waveguide. Our analysis reveals a strong enhancement of the scattering when the energy of incoming photons resonates with the double-excited subradiant states. We identify the role of different double-excited states in the scattering, such as superradiant, subradiant, and twilight states, as a product of single-excitation bright and subradiant states. Importantly, the N-excitation subradiant states can be engineered only if the number of qubits exceeds 2N. Both the subradiant and twilight states can generate long-lived photon-photon correlations, paving the way to storage and processing of quantum information.

Photon–photon correlations with a V-type three-level system interacting with two quantized field modes

We carry out a model study on the interaction of a $V$-type three-level emitter with two quantized cavity modes which are weakly driven by two classical fields. The emitter may be an atom or a molecule with nondegenerate upper levels in general. The lifetimes of the two upper levels are assumed to be much longer than the lifetime of the cavity photons. We calculate the two-time second order coherence function, namely Hanbury Brown-Twiss function $g^{(2)}(\tau)$ where $\tau$ is the time delay between the two modes. We analyze the photon-photon correlations between the two cavity modes in terms of $g^{(2)}(\tau)$. The variation of $g^{(2)}(\tau)$ as a function of $\tau$ exhibits collapse and revival type oscillations as well as quantum beats for relatively short $\tau$ while in the limit $\tau \rightarrow \infty$, $g^{(2)}(\tau) \simeq 1$. We further show that the two cavity field modes are entangled when $g^{(2)}(0) > 2$. We develop a dressed state picture with single photon in each mode to explain the results and use the negativity of the partial transpose of the reduced field density matrix to show the entanglement between field modes. The model presented in this paper may be useful for generating entangled photon pairs, and also manipulating photon-photon correlations with a cavity QED set up.

Photon transport mediated by an atomic chain trapped along a photonic crystal waveguide

We theoretically investigate the transport properties of a weak coherent input field scattered by an ensemble of $\Lambda$-type atoms coupled to a one-dimensional photonic crystal waveguide. In our model, the atoms are randomly located in the lattice along the crystal axis. We analyze the transmission spectrum mediated by the tunable long-range atomic interactions, and observe the highest-energy dip. The results show that the highest-energy dip location is associated with the number of the atoms, which provides an accurate measuring tool for the emitter-waveguide system. We also quantify the influence of a Gaussian inhomogeneous broadening and the dephasing on the transmission spectrum, concluding that the highest-energy dip is immune to both the inhomogeneous broadening and the dephasing. Furthermore, we study photon-photon correlations of the reflected field and observe quantum beats. With tremendous progress in coupling atoms to photonic crystal waveguides, our results may be experimentally realizable in the near future.

Protocol for generating multiphoton entangled states from quantum dots in the presence of nuclear spin fluctuations

Multi-photon entangled states are a crucial resource for many applications in quantum information science. Semiconductor quantum dots offer a promising route to generate such states by mediating photon-photon correlations via a confined electron spin, but dephasing caused by the host nuclear spin environment typically limits coherence (and hence entanglement) between photons to the spin $T_2^*$ time of a few nanoseconds. We propose a protocol for the deterministic generation of multi-photon entangled states that is inherently robust against the dominating slow nuclear spin environment fluctuations, meaning that coherence and entanglement is instead limited only by the much longer spin $T_2$ time of microseconds. Unlike previous protocols, the present scheme allows for the generation of very low error probability polarisation encoded three-photon GHZ states and larger entangled states, without the need for spin echo or nuclear spin calming techniques.

Quantum cascade driving: Dissipatively mediated coherences

Quantum cascaded systems offer the possibility to manipulate a target system with the quantum state of a source system. Here, we study in detail the differences between a direct quantum cascade and coherent/incoherent driving for the case of two coupled cavity-QED systems. We discuss qualitative differences between these excitations scenarios, which are particular strong for higher-order photon-photon correlations: $g^{(n)}(0)$ with $ n>2 $. Quantum cascaded systems show a behavior differing from the idealized cases of individual coherent/incoherent driving and allow to produce qualitatively different quantum statistics. Furthermore, the quantum cascaded driving exhibits an interesting mixture of quantum coherent and incoherent excitation dynamics. We develop a measure, where the two regimes intermix and quantify these differences via experimentally accessible higher-order photon correlations.

Photon Emissions from a Spinor Bose–Einstein Condensate of Positroniums**Supported by National Natural Science Foundation of China under Grant Nos. 11434011, 11674334, 11421063, and 11674393, National Key Basic Research Special Foundation of China under Grant No. 2012CB922104, the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China under Grant Nos. 16XNLQ03 and 17XNH054

We investigate the quantum dynamics of the decay of a multiple-component positronium condensate into pairs of photons. A positronium atom has four internal spin states which are interconvertible through s-wave interactions. The quantum fields of all spin states of positroniums and photons are simulated from first principle in quasi-one-dimensional system using the truncated Wigner method. This method warrants us a full treatment of the depletion of positronium fields and the spin mixing induced by s-wave collisions between positronium atoms. Particularly, it yields the momentum spectrum of the emitted photons and the photon-photon correlations.

Highly efficient two-photon generation from a coherently pumped quantum dot embedded in a microcavity

We propose a scheme to realize a highly efficient solid state source of photon pairs using cavity-assisted stimulated Raman adiabatic passage (STIRAP) in a single quantum dot, where a single photon from pump pulse and two stokes photons from cavity mode drives the Raman transition. The Autler-Townes doublet, generated by using a resonant continuous wave laser between biexciton and exciton states, and two-photon-resonant transition through strongly coupled cavity mode are utilized to facilitate (1+2)type Raman transition in the quantum dot. We show in the case of weak pump although the probability of generating two photons in cavity mode is small without cavity damping but two-photon-resonant emission is enhanced by cavity damping within strong coupling regime. We also discuss spectrum of the generated photon pair and photon-photon correlations in the generated photon pair. The efficiency of two photon source could be more than 80\% in current experimental conditions.

Green's-function formalism for waveguide QED applications

We present a quantum-field-theoretical framework based on path integrals and Feynman diagrams for the investigation of the quantum-optical properties of one-dimensional waveguiding structures with embedded quantum impurities. In particular, we obtain the Green's functions for a waveguide with an embedded two-level system in the single- and two-excitation sector for arbitrary dispersion relations. In the single excitation sector, we show how to sum the diagrammatic perturbation series to all orders and thus obtain explicit expressions for physical quantities such as the spectral density and the scattering matrix. In the two-excitation sector, we show that strictly linear dispersion relations exhibit the special property that the corresponding diagrammatic perturbation series terminates after two terms, again allowing for closed-form expressions for physical quantities. In the case of general dispersion relations, notably those exhibiting a band edge or waveguide cut-off frequencies, the perturbation series cannot be summed explicitly. Instead, we derive a self-consistent T-matrix equation that reduces the computational effort to that of a single-excitation computation. This analysis allows us to identify a Fano resonance between the occupied quantum impurity and a free photon in the waveguide as a unique signature of the few-photon nonlinearity inherent in such systems. In addition, our diagrammatic approach allows for the classification of different physical processes such as the creation of photon-photon correlations and interaction-induced radiation trapping - the latter being absent for strictly linear dispersion relations. Our framework can serve as the basis for further studies that involve more complex scenarios such as several and many-level quantum impurities, networks of coupled waveguides, disordered systems, and non-equilibrium effects.

Superbunching and Nonclassicality as new Hallmarks of Superradiance.

Superradiance, i.e., spontaneous emission of coherent radiation by an ensemble of two-level atoms in collective states introduced by Dicke in 1954, is one of the enigmatic problems of quantum optics. The startling gist is that even though the atoms have no dipole moment they radiate with increased intensity in particular directions. Following the advances in our understanding of superradiant emission by atoms in entangled W-states we examine the quantum statistical properties of superradiance. Such investigations require the system to have at least two excitations in order to explore the photon-photon correlations of the radiation emitted by such states. We present specifically results for the spatially resolved photon-photon correlations of systems prepared in doubly excited W-states and give conditions when the atomic system emits nonclassial light. Equally, we derive the conditions for the occurrence of bunching and even of superbunching, a rare phenomenon otherwise known only from nonclassical states of light like the squeezed vacuum. We finally investigate the photon-photon cross correlations of the spontaneously scattered light and highlight the nonclassicalty of such correlations. The theoretical findings can be implemented with current technology, e.g., using ions in a linear rf-trap, atoms in an optical lattice or quantum dots in a cavity.

Operating Spin Echo in the Quantum Regime for an Atomic-Ensemble Quantum Memory.

Spin echo is a powerful technique to extend atomic or nuclear coherence times by overcoming the dephasing due to inhomogeneous broadenings. However, there are disputes about the feasibility of applying this technique to an ensemble-based quantum memory at the single-quanta level. In this experimental study, we find that noise due to imperfections of the rephasing pulses has both intense superradiant and weak isotropic parts. By properly arranging the beam directions and optimizing the pulse fidelities, we successfully manage to operate the spin echo technique in the quantum regime by observing nonclassical photon-photon correlations as well as the quantum behavior of retrieved photons. Our work for the first time demonstrates the feasibility of harnessing the spin echo method to extend the lifetime of ensemble-based quantum memories at the single-quanta level.

One-dimensional waveguide coupled to multiple qubits: photon-photon correlations

For a one-dimensional (1D) waveguide coupled to two or three qubits, we show that the photon-photon correlations have a wide variety of behavior, with structure that depends sensitively on the frequency and on the qubit-qubit separation $L$. We study the correlations by calculating the second-order correlation function $g_2(t)$ in which the interference among the photons multiply scattered from the qubits causes rich structure. In one case, for example, transmitted and reflected photons are both bunched initially, but then become strongly anti-bunched for a long time interval. We first calculate the correlation function $g_2(t)$ including non-Markovian effects and then show that a much simpler Markovian treatment, which can be solved analytically, is accurate for small qubit separation. As a result, the non-classical properties of microwaves in a 1D waveguide coupled to many superconducting qubits with experimentally accessible separation $L$ could be readily explored with our approach.