Photon Correlation Function Research Articles

Fiber-pigtailed optical tweezer for single-atom trapping and single-photon generation

We demonstrate a miniature, fiber-coupled optical tweezer to trap a single atom. The same fiber is used to trap a single atom and to read out its fluorescence. To obtain a low background level, the tweezer light is chopped, and we measure the influence of the chopping frequency on the atom's lifetime. We use the single atom as a single-photon source at 780 nm and measure the second-order correlation function of the emitted photons. Because of its miniature, robust, fiber-pigtailed design, this tweezer can be implemented in a broad range of experiments where single atoms are used as a resource.

Photon blockade in quadratically coupled optomechanical systems

We study the steady-state photon statistics of a quadratically coupled optomechanical cavity, which is weakly driven by a monochromatic laser field. We examine the photon blockade by evaluating the second-order correlation function of the cavity photons. By restricting the system within the zero-, one-, and two-photon subspace, we obtain an approximate analytical expression for the correlation function. We also numerically investigate the correlation function by solving the quantum master equation including both optical and mechanical dissipations. The results show that, in the deep-resolved-sideband and single-photon strong-coupling regimes, the single-photon resonant driving will induce a photon blockade, which is limited by the thermal noise of the mechanical environment.

Enhanced photon correlations due to strong laser-atom-cavity coupling

We investigate the resonant quantum dynamics of a laser-pumped real or artificial two-level single-atom system embedded in a leaking microcavity. We found that for stronger laser-atom-cavity couplings the generated microcavity photons exhibit larger steady-state correlations. In particular, the second- and third-order photon correlation functions are greater than the corresponding ones obtained for an incoherent light source, respectively. Furthermore, the emitted microcavity photon flux is enhanced in comparison to weaker coupling cases.

Dicke-model quantum spin and photon glass in optical cavities: Nonequilibrium theory and experimental signatures

In the context of ultracold atoms in multimode optical cavities, the appearance of a quantum-critical glass phase of atomic spins has been predicted recently. Due to the long-range nature of the cavity-mediated interactions, but also the presence of a driving laser and dissipative processes such as cavity photon loss, the quantum optical realization of glassy physics has no analog in condensed matter and could evolve into a ``cavity glass microscope'' for frustrated quantum systems out of equilibrium. Here we develop the nonequilibrium theory of the multimode Dicke model with quenched disorder and Markovian dissipation. Using a unified Keldysh path integral approach, we show that the defining features of a low-temperature glass, representing a critical phase of matter with algebraically decaying temporal correlation functions, are seen to be robust against the presence of dissipation due to cavity loss. The universality class, however, is modified due to the Markovian bath. The presence of strong disorder leads to an enhanced equilibration of atomic and photonic degrees of freedom, including the emergence of a common low-frequency effective temperature. The imprint of the atomic spin-glass physics onto the photon subsystem realizes a ``photon glass'' state and makes it possible to detect the glass state by standard experimental techniques of quantum optics. We provide an unambiguous characterization of the superradiant and glassy phases in terms of fluorescence spectroscopy, homodyne detection, and the temporal photon correlation function ${g}^{(2)}(\ensuremath{\tau})$.

Photon-number-resolved detection of photon-subtracted thermal light

We examine the photon statistics of photon-subtracted thermal light using photon-number-resolved detection. We demonstrate experimentally that the photon number distribution transforms from a Bose-Einstein distribution to a Poisson distribution as the number of subtracted photons increases. We also show that second- and higher-order photon correlation functions can be directly determined from the photon-number-resolved detection measurements of a single optical beam.

Correlated two-photon scattering in cavity optomechanics

We present an exact analytical solution of the two-photon scattering in a cavity optomechanical system. This is achieved by solving the quantum dynamics of the total system, including the optomechanical cavity and the cavity-field environment, with the Laplace transform method. The long-time solution reveals detailed physical processes involved as well as the corresponding resonant photon frequencies. We characterize the photon correlation induced in the scattering process by calculating the two-photon joint spectrum of the long-time state. Clear evidence for photon frequency anti-correlation can be observed in the joint spectrum. In addition, we calculate the equal-time second-order correlation function of the cavity photons. The results show that the radiation pressure coupling can induce photon blockade effect, which is strongly modulated by the phonon sideband resonance. In particular, we obtain an explicit expression of optomechanical coupling strength determining these sideband modulation peaks based on the two-photon resonance condition.

Incoherent excitation of few-level multi-atom ensembles

We investigate the collective interaction of a multi-atom three-level ladder system with an environmental incoherent reservoir. The exact solution of the master equation that describes such a system of atoms emitting distinguishable or indistinguishable photons on interaction with an incoherent reservoir is obtained. The quantum decay interference effects have no influence over the steady-state distribution of population among the energy levels. However, the photon statistics of the collectively emitted photons are different in this case. In particular, the normalized second-order photon correlation function shows a minimum in its value for the photons generated on lower atomic transition in a system with orthogonal dipoles. The minimum is due to the steady-state amplified spontaneous emission by the incoherent applied fields.

Multiphoton quantum interference in a multiport integrated photonic device

Increasing the complexity of quantum photonic devices is essential for many optical information processing applications to reach a regime beyond what can be classically simulated, and integrated photonics has emerged as a leading platform for achieving this. Here we demonstrate three-photon quantum operation of an integrated device containing three coupled interferometers, eight spatial modes and many classical and nonclassical interferences. This represents a critical advance over previous complexities and the first on-chip nonclassical interference with more than two photonic inputs. We introduce a new scheme to verify quantum behaviour, using classically characterised device elements and hierarchies of photon correlation functions. We accurately predict the device's quantum behaviour and show operation inconsistent with both classical and bi-separable quantum models. Such methods for verifying multiphoton quantum behaviour are vital for achieving increased circuit complexity. Our experiment paves the way for the next generation of integrated photonic quantum simulation and computing devices.

Quantum dot-DNA origami binding: a single particle, 3D, real-time tracking study

The binding process of quantum dots and DNA origami was monitored using a 3D, real-time, single-particle tracking system. Single-molecule binding events were directly observed and precise measurements of the diffusion coefficient and second-order photon correlation function, g(2)(τ), were combined to distinguish free quantum dots from different conjugates of nQdot-origami.

Coherent state path integral approach to multi-time correlation functions and photon emission in a semiconductor microcavity

In this paper by using the coherent state path integral field theory approach, we calculate the grand canonical partition function of an interacting combined system in the presence of the relevant source terms. It allows us to calculate multi-time correlation functions of interacting systems without using the quantum regression theorem. Then, we investigate the power spectrum and the second-order correlation function of the emitted photons from a microcavity in the presence of excitations of a semiconductor quantum well. By using the Hubbard–Stratonovich transformation, we investigate the effects of reservoir, detuning, the Coulomb interaction and the phase space filling on the power spectrum and the second-order correlation function of the emitted photons.

Single-Photon Emission and Quantum Characterization of Zinc Oxide Defects

Room temperature single-photon emission and quantum characterization is reported for isolated defects in zinc oxide. The defects are observed in thin films of both in-house synthesized and commercial zinc oxide nanoparticles. Emission spectra in the red and infrared, second-order photon correlation functions, lifetime measurements, and photon count rates are presented. Both two- and three-state emitters are identified. Sub-band gap absorption and red emission suggest these defects are the zinc vacancy. These results identify a new source of single photons in a readily available wide band gap semiconductor material which has exceptional electrical, optical, and biocompatibility properties.

Photon–quantum-dot dynamics in coupled-cavity photonic crystal slabs

We derive a master equation for the total-system density matrix to treat the evolution of quantum dots and photons in a photonic crystal slab with multiple, coupled, lossy defect cavities. In such systems, when the resonant lossy quasimodes of the system overlap in frequency and space, they are generally nonorthogonal. We find that this nonorthogonality can have important consequences for the system evolution. Our formalism allows for the calculation of multiple-photon effects in the presence of quasimode nonorthogonality. It can be applied to the calculation of strong- and weak-coupling dynamics and to first- and second-order photon correlation functions in a wide variety of complicated coupled-cavity systems. As an example, we apply the formalism to an asymmetric two-cavity photonic crystal slab and demonstrate how quasimode nonorthogonality results in oscillations in the decay of the photons out of the system.

Cooperative scattering effect between Stokes and anti-Stokes field stimulated by a stream of atoms

This paper is devoted to the study of the cooperative two-photon scattering processes between two resonator modes stimulated by an excited atomic beam. It has been proved that these collective scattering phenomena between the Stokes and anti-Stokes resonator modes are taking place due to the energy transfer between these fields. The statistical properties of the Stokes and anti-Stokes photons have been described using the photon correlation functions. The numerical solution of this equation describes the statistical transformation of n-Stokes photons into anti-Stokes photons.

Lasing properties of InP/(Ga0.51In0.49)P quantum dots in microdisk cavities

We investigated the photoluminescence from InP quantum dots incorporated in (Ga${}_{0.51}$In${}_{0.49}$)P microdisk structures. With increasing pump power we observe a transition to stimulated emission indicated by the S shape of the input-output curve. This transition is accompanied with a concentration of the emission to one or a few modes exhibiting quality factors on the order of ${10}^{4}$ at transparency. Time-resolved measurements show that at the same time the photoluminescence decay time considerably decreases. Furthermore, in the transition regime the linewidth of the lasing mode is reduced and the second-order photon correlation function exhibits a reduction of fluctuations as previously reported for lasers with InAs quantum dots in photonic crystal, microdisk and micropillar cavities as the gain medium. The experimental findings are compared with the predictions of a microscopic theory.

Angle-resolved photon-coincidence measurements in a multiple-scattering medium

We present angular-resolved correlation measurements between photons after propagation through a three-dimensional disordered medium. The multiple scattering process induces photon correlations that are directly measured for light sources with different photon statistics. We find that multiple scattered photons between different angular directions with angles much larger than the average speckle width are strongly correlated. The time dependence of the angular photon correlation function is investigated and the coherence time of the light source is determined. Our results are found to be in excellent agreement with the continuous mode quantum theory of multiple scattering of light. The presented experimental technique is essential in order to study quantum phenomena in multiple scattering random media such as quantum interference and quantum entanglement of photons.

Mesoscopic admittance of a double quantum dot

We calculate the mesoscopic admittance $G(\omega)$ of a double quantum dot (DQD),which can be measured directly using microwave techniques. This quantity reveals spectroscopic information on the DQD and is also directly sensitive to a Pauli spin blockade effect. We then discuss the problem of a DQD coupled to a high quality photonic resonator. When the photon correlation functions can be developed along a random-phase-approximation-like scheme, the response of the resonator gives an access to $G(\omega)$.

Quantum interference and non-locality of independent photons from disparate sources

We quantitatively investigate the non-classicality and non-locality of a whole new class of mixed disparate quantum and semiquantum photon sources at the quantum–classical boundary. The latter include photon-added thermal and photon-added coherent sources, experimentally investigated recently by Zavatta et al (2009 Phys. Rev. Lett. 103 140406). The key quantity in our investigations is the visibility of the corresponding photon–photon correlation function. We present explicit results on the violations of the Cauchy–Schwarz inequality—which is a measure of non-classicality—as well as of Bell-type inequalities.

Schemes for the observation of photon correlation functions in circuit QED with linear detectors

Correlations are important tools in the characterization of quantum fields. They can be used to describe statistical properties of the fields, such as bunching and anti-bunching, as well as to perform field state tomography. Here we analyse experiments by Bozyigit et al. [arXiv:1002.3738] where correlation functions can be observed using the measurement records of linear detectors (i.e. quadrature measurements), instead of relying on intensity or number detectors. We also describe how large amplitude noise introduced by these detectors can be quantified and subtracted from the data. This enables, in particular, the observation of first- and second-order coherence functions of microwave photon fields generated using circuit quantum-electrodynamics and propagating in superconducting transmission lines under the condition that noise is sufficiently low.

Phase sensitive two-mode squeezing and photon correlations from exciton superfluid in semiconductor electron-hole bilayer systems

There have been experimental and theoretical studies on Photoluminescence (PL) from possible exciton superfluid in semiconductor electron-hole bilayer systems. However, the PL contains no phase information and no photon correlations, so it can only lead to suggestive evidences. It is important to identify smoking gun experiments which can lead to convincing evidences. Here we study two mode phase sensitive squeezing spectrum and also two photon correlation functions. We find the emitted photons along all tilted directions are always in a two mode squeezed state between $ \vec{k} $ and $ - \vec{k} $. There are always two photon bunching, the photon statistics is super-Poissonian. Observing these unique features by possible future phase sensitive homodyne experiment and HanburyBrown-Twiss type of experiment could lead to conclusive evidences of exciton superfluid in these systems.

Effect of an atom on a quantum guided field in a weakly driven fiber-Bragg-grating cavity

We study the interaction of an atom with a quantum guided field in a weakly driven fiber-Bragg-grating (FBG) cavity. We present an effective Hamiltonian and derive the density-matrix equations for the combined atom-cavity system. We calculate the mean photon number, the second-order photon correlation function, and the atomic excited-state population. We show that, due to the confinement of the guided cavity field in the fiber cross-section plane and in the space between the FBG mirrors, the presence of the atom in the FBG cavity can significantly affect the mean photon number and the photon statistics even though the cavity finesse is moderate, the cavity is long, and the probe field is weak.