We report measurements of an intensity-field correlation function of the resonance fluorescence of a single trapped Ba+ ion. Detection of a photon prepares the atom in its ground state and we observe its subsequent evolution under interaction with a laser field of well defined phase. We record the regression of the resonance fluorescence source field. This provides a direct measurement of the field of the radiating dipole of a single atom and exhibits its strong non-classical behavior. In the experimental setup an interference measurement is conditioned on a fluorescence photon detection. The third-order correlation function thus recorded demonstrates an aspect of wave-particle duality at the single-atom, single-photon level.
We investigate intensity of the parametric down conversion of ultrashort, ultraviolet pulse both in a low- and high-conversion regime. In the first regime, we develop a simple analytical expressions for the photon flux of the fluorescence. Numerical simulations using three-dimensional stochastic Wigner method provide results in the latter regime. We find that the perturbative approximation for the photon flux as a function of the wavelength of the signal and the observation angle, quantitatively describes even the non-perturbative regime. For short pump pulses the intensity of the fluorescence…
In this paper we show that the scattered field of a bichromatically driven V-type three-level atom exhibit asymmetry and large violation of classical bounds in amplitude-intensity correlations. These features result from the noncommutativity of amplitude and intensity field operators, and the strong non-Gaussian fluctuations in this system. The amplitude-intensity correlations of resonance fluorescence, with its large third-order fluctuations, describe the nonclassical features of the emitted field more accurately than the second-order measure related to squeezing. Spectra and variances of the…
We explore the fluorescence signals from a pair of atoms driven towards Rydberg states on a three-level ladder transition. The dipole--dipole interactions between Rydberg excited atoms significantly distort the dark state and electromagnetically induced transparency behavior observed with independent atoms and, thus, their steady state light emission. We calculate and analyze the temporal correlations between intensities and amplitudes of the signals emitted by the atoms and explain their origin in the atomic Rydberg state interactions.
We demonstrate how optical nanofibers can be used to manipulate and probe single-atom fluorescence. We show that fluorescence photons from a very small number of atoms, average atom number of less than 0.1, around the nanofiber can readily be observed through single-mode optical fiber under resonant laser irradiation. We show also that optical nanofibers enable us to probe the van der Waals interaction between atoms and surface with high precision by observing the fluorescence excitation spectrum.
The resonance fluorescence from regular atomic systems is shown to represent a continuous source of non-Gaussian entangled radiation propagating in two different directions. For a single atom entanglement occurs under the same conditions as squeezing. For more atoms, the entanglement can be more robust against dephasing than squeezing, hence providing a useful continuous source for various applications of entangled radiation.
We present an experimental realization of resonance fluorescence in squeezed vacuum. We strongly couple microwave-frequency squeezed light to a superconducting artificial atom and detect the resulting fluorescence with high resolution enabled by a broadband traveling-wave parametric amplifier. We investigate the fluorescence spectra in the weak and strong driving regimes, observing up to 3.1 dB of reduction of the fluorescence linewidth below the ordinary vacuum level and a dramatic dependence of the Mollow triplet spectrum on the relative phase of the driving and squeezed vacuum fields. Our r…
Steady-state fluorescence spectra of a two-level atom embedded in a three-dimensional photonic bandgap crystal and driven by a monochromatic classical electrical field is calculated theoretically for the first time as we know. The non-Markovian noises caused by the non-uniform distribution of photon density of states near the photonic bandgap are handled by a new approach in which the Liouville operator expansion is utilized to linearize the generalized optical Bloch equations. The fluorescence spectra are then directly solved by the linearized Bloch equations in the frequency domain. We find …
Squeezing of atomic resonance fluorescence is shown to be optimized by a properly designed environment, which can be realized by a quasi-resonant cavity. Optimal squeezing is achieved if the atomic coherence is maximized, corresponding to a pure atomic quantum state. The atomic-state purification is achieved by the backaction of the cavity field on the atom, which increases the atomic coherence and decreases the atomic excitation. For realistic cavities, the coupling of the atom to the cavity field yields a purity of the atomic state of more than 99%. The fragility of squeezing against dephasi…
Intensity squeezing, i.e., photon number fluctuations below the shot noise limit, is a fundamental aspect of quantum optics and has wide applications in quantum metrology. It was predicted in 1979 that the intensity squeezing could be observed in resonance fluorescence from a two-level quantum system. Yet, its experimental observation in solid states was hindered by inefficiencies in generating, collecting and detecting resonance fluorescence. Here, we report the intensity squeezing in a single-mode fibre-coupled resonance fluorescence single-photon source based on a quantum dot-micropillar sy…
We study the processes in a quantum dot and its surrounds under resonant excitation with the addition of weak non-resonant light. We observe a decrease in inhomogeneous emission linewidth, as well as previously observed enhancement of resonant fluorescence (RF). Scanning excitation and detection frequencies, we distinguish between homogeneous and inhomogeneous broadening. Monte Carlo simulations model the enhanced RF only if we include charge-carrier loss from the quantum dot induced by the resonant laser. The cause of the linewidth narrowing is predominantly independent of the enhanced RF.
A cavity-modified master equation is derived for a coherently driven, V-type three-level atom coupled to a single-mode cavity in the bad cavity limit. We show that population inversion in both the bare and dressed-state bases may be achieved, originating from the enhancement of the atom-cavity interaction when the cavity is resonant with an atomic dressed-state transition. The atomic populations in the dressed state representation are analysed in terms of the cavity-modified transition rates. The atomic fluorescence spectrum and probe absorption spectrum also investigated, and it is found that…
We investigate a single laser driven atom trapped in a non-harmonic potential. We present the performance of ground-state laser cooling and Doppler cooling and the signatures of the center-of-mass motion in the power spectrum of the scattered light. In order to illustrate the results we provide two explicit examples for the confining potential: the infinite square well and the Morse potential.
Resonance fluorescence from atomic systems consists of a single spectral peak that evolves into a Mollow triplet for a strong excitation field. Photons from different peaks of the triplet show distinct photon correlation that make the fluorescence a useful light source for quantum information purpose. We characterize the fluorescence of a single optically trapped $^{87}$Rb atom that is excited resonantly at different power levels. Second-order correlation measurements reveal the single photon nature of the fluorescence concurrently with Rabi oscillations of a strongly excited atom. The asymmet…
Photon correlations are investigated for a single laser-excited ion trapped in front of a mirror. Varying the relative distance between the ion and the mirror, photon correlation statistics can be tuned smoothly from an antibunching minimum to a bunching-like maximum. Our analysis concerns the non-Markovian regime of the ion-mirror interaction and reveals the field establishment in a half-cavity interferometer.
We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are $Λ$--shaped and driven at two-photon resonance by a pair of lasers, which cool the center--of--mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser--cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb--Dicke limit). …
The resonance fluorescence of a four-level atom in J = 1/2 to J = 1/2 transition driven by two coherent fields is studied. We find that the incoherent fluorescence spectrum shows a direct indication of vacuum-induced coherence in the atomic system. We show that such coherence manifests itself via an enhancement or suppression of the spectral peaks in the $π$-polarized fluorescence. The effect of the relative phase of the driving fields on the spectral features is also investigated. We show that phase-dependent enhancement or suppression of the fluorescence peaks appears in the incoherent spect…
We present a formula to evaluate the spontaneous emission spectra of an atom in contact with a radiation field with non-Markovian effects. This formula is written in terms of a two-time correlation of system observables and the environmental correlation function, and depends on the distance between the emitting atom and the detector. As an example, we use it to analyze the fluorescence spectra of a two level atom placed as an impurity in a photonic crystal. The radiation field within those materials has a gap or discontinuity where electromagnetic modes cannot propagate in the stationary limit…
We investigate an atomic $Λ$-system with one transition coupled to a laser field and a flat continuum of vacuum modes and the other transition coupled to field modes near the edge of a photonic band gap. The system requires simultaneous treatment of Markovian and non-Markovian dissipation processes, but the photonic band gap continuum can not be eliminated within a density matrix treatment. Instead we propose a formalism based on Monte-Carlo wavefunctions, and we present results relevant to an experimental characterization of a structured continuum.
We consider a two-level atom stimulated by a coherent monochromatic laser and we study how to enhance the squeezing of the fluorescence light and of the atom itself in the presence of a Wiseman-Milburn feedback mechanism, based on the homodyne detection of a fraction of the emitted light. Besides analyzing the effect of the control parameters on the squeezing properties of the light and of the atom, we also discuss the relations among these. The problem is tackled inside the framework of quantum trajectory theory.
The squeezing spectrum of the fluorescence field emitted from a four-level atom in $J=1/2$ to $J=1/2$ configuration driven by two coherent fields is studied. We find that the squeezing properties of the fluorescence radiation are significantly influenced by the presence of vacuum-induced coherence in the atomic system. It is shown that such coherence induces spectral squeezing in phase quadratures of the fluorescence light for both weak and strong driving fields. The dependence of the squeezing spectrum on the relative phase of the driving fields is also investigated. Effects such as enhanceme…
We adopt an open quantum systems perspective to calculate the power spectrum associated with the electric field generated by an atomic dipole moment undergoing resonant laser-driving. This spectrum has a similar shape to the usual Mollow spectrum, but also has some distinct features. For sufficiently strong laser driving, both spectra have a symmetric triplet structure with a large central peak and two sidebands. However, the relative height of the sidebands to the central peak differs in each case. The two spectra also behave quite differently when the laser Rabi frequency is varied. Both spe…
The fluorescence spectrum of a strongly pumped two level system is characterised by the Mollow triplet that has been observed in a variety of systems, ranging from atoms to quantum dots and superconducting qubits. We theoretically studied the fluorescence of a strongly pumped intersubband transition in a quantum well. Our results show that the many-electron nature of such a system leads to a modification of the usual Mollow theory. In particular, the intensity of the central peak in the fluorescence spectrum becomes a function of the electron coherence, allowing access to the coherence time of…
An operational arrival-time distribution is defined as the distribution of detection times of the first photons emitted by two level atoms in resonance with a perpendicular laser beam in a time of flight experiment. For ultracold Cesium atoms the simulations are in excellent agreement with the theoretical ideal time-of-arrival distribution of Kijowski.
The fluorescence intensity and quadrature spectra from a two-level atom embedded in a photonic bandgap crystal and resonantly driven by a classical pump light are calculated. The non-Markovian nature of the problem caused by the non-uniform distribution of the photonic density of states is handled by linearizing the generalized optical Bloch equations with the Liouville operator expansion. Unlike the case in free space, we find that the bandgap effects will not only modify the fluorescence spectral shape but also cause squeezing in the in-phase quadrature spectra.
It is shown that 100% squeezed output can be produced in the resonance fluorescence from a coherently driven two-level atom interacting with a squeezed vacuum. This is only possible for $N=1/8$ squeezed input, and is associated with a pure atomic state, i.e., a completely polarized state. The quadrature for which optimal squeezing occurs depends on the squeezing phase $Φ,$ the Rabi frequency $Ω,$ and the atomic detuning $Δ$. Pure states are described for arbitrary $Φ,$ not just $Φ=0$ or $π$ as in previous work. For small values of $N,$ there may be a greater degree of squeezing in the output f…
We present a conditional quantum eraser which erases the a priori knowledge or the predictability of the path a photon takes in a Young-type double-slit experiment with two fluorescent four-level atoms. This erasure violates a recently derived erasure relation which must be satisfied for a conventional, unconditional quantum eraser that aims to find an optimal sorting of the system into subensembles with particularly large fringe visibilities. The conditional quantum eraser employs an interaction-free, partial which-way measurement which not only sorts the system into optimal subsystems with l…
We experimentally demonstrate an atom number detector capable of simultaneous detection of two mesoscopic ensembles with single-atom resolution. Such a sensitivity is a prerequisite for quantum metrology at a precision approaching the Heisenberg limit. Our system is based on fluorescence detection of atoms in a novel hybrid trap in which a dipole barrier divides a magneto-optical trap into two separated wells. We introduce a noise model describing the various sources contributing to the measurement error and report a limit of up to 500 atoms for single-atom resolution in the atom number differ…
We theoretically study the occurrence of quantum jumps in the resonance fluorescence of a trapped atom. Here, the atom is laser cooled in a configuration of level such that the occurrence of a quantum jump is associated to a change of the vibrational center-of-mass motion by one phonon. The statistics of the occurrence of the dark fluorescence period is studied as a function of the physical parameters and the corresponding features in the spectrum of resonance fluorescence are identified. We discuss the information which can be extracted on the atomic motion from the observation of a quantum j…
This proposal investigates the photon-statistics of light emitted by a statistical ensemble of cold atoms excited by the near-field of an optical nanofiber tip. Dipole-dipole interactions of atoms at such short distance from each other suppress the simultaneous emission of more than one photon and lead to antibunching of photons. We consider a mean atom number on the order of one and deal with a poissonian mixture of one and two atoms including dipole-dipole interactions and collective decay. Time tracks of the atomic states are simulated in quantum Monte Carlo simulations from which the $g^{(…
We study the resonance fluorescence in the Jaynes-Cummings model when nearby levels are taking into account. We show that the Stark shift produced by such levels generates a displacement of the peaks of the resonance fluorescence due to an induced effective detuning and also induces an asymmetry. Specific results are presented assuming a coherent and a thermal fields.
Measuring the amplitude and the absolute phase of a monochromatic microwave field at a specific point of space and time has many potential applications, including precise qubit rotations and wavelength quantum teleportation. Here we show how such a measurement can indeed be made using resonant atomic probes, via detection of incoherent fluorescence induced by a laser beam. This measurement is possible due to self-interference effects between the positive and negative frequency components of the field. In effect, the small cluster of atoms here act as a highly localized pick-up coil, and the fl…
We investigate fluorescence detection using a standing wave of blue-detuned light of one or more atoms held in a deep, microscopic dipole trap. The blue-detuned standing wave realizes a Sisyphus laser cooling mechanism so that an atom can scatter many photons while remaining trapped. When imaging more than one atom, the blue detuning limits loss due to inelastic light-assisted collisions. Using this standing wave probe beam, we demonstrate that we can count from one to the order of 100 atoms in the microtrap with sub-poissonian precision.
Atomic detection by fluorescence may fail because of reflection from the laser or transmission without excitation. The detection probability for a given velocity range may be improved by controlling the detuning and the spatial dependence of the laser intensity. A simple optimization method is discussed and exemplified.
We experimentally investigate the resonance fluorescence spectrum of single 171Yb and 172Yb ions which are laser cooled to the Lamb-Dicke regime in a radiofrequency trap. While the fluorescence scattering of 172Yb is continuous, the 171Yb fluorescence is interrupted by quantum jumps because a nonvanishing rate of spontaneous transitions leads to electron shelving in the metastable hyperfine sublevel 2D3/2(F=2). The average duration of the resulting dark periods can be varied by changing the intensity of a repumping laser field. Optical heterodyne detection is employed to analyze the fluorescen…
We investigate the effect of strong interaction in the dressed energy levels of the two level emitters. Strong dipole-dipole interactions give rise to new sidebands in the fluorescence spectrum due to specific couplings among the collective dressed levels which in turn depends on the spatial configuration of atoms. These couplings are the main responsible for the frequencies and variety of sidebands. We explain the general method for finding the dressed energy levels for a system of any number of strongly coupled atoms and we solve this problem for two different spatial configurations of three…
The squeezing spectrum of the resonance fluorescence is studied for a coherently driven four-level atom in the Y-type configuration. It is found that the squeezing properties of the fluorescence radiation are modified significantly when quantum interference of the spontaneous decays channels is included. We show a considerable enhancement of steady-state squeezing in spectral components for strong and off-resonant driving fields. The squeezing may be increased in both the inner and outer sidebands of the spectrum depending upon the choice of parameters. We also show that the interference can d…
Supplementary information is presented on the recent work by W. Kim et al. on the matter-wave-tunneling-induced broadening in the near-resonant spectra of a single rubidium atom localized in a three-dimensional optical lattice in a strong Lamb-Dicke regime.
The ignition of two-quantum collective emission of inverted sub-ensemble of radiators due to mutual interaction of this sub-ensemble with other two dipole active atomic subsystems in process of two-photon exchanges between the atoms through the vacuum field is proposed. The three particle resonances between two-photon and single quantum transitions of inverted radiators from the ensemble are proposed for acceleration of collective decay rate of bi-photons, obtained relatively dipole-forbidden transitions of excited atomic sub-ensemble. This mutual interaction between three super-fluorescent pr…
It has been observed experimentally [H.R. Xia, C.Y. Ye, and S.Y. Zhu, Phys. Rev. Lett. {\bf 77}, 1032 (1996)] that quantum interference between two molecular transitions can lead to a suppression or enhancement of spontaneous emission. This is manifested in the fluorescent intensity as a function of the detuning of the driving field from the two-photon resonance condition. Here we present a theory which explains the observed variation of the number of peaks with the mutual polarization of the molecular transition dipole moments. Using master equation techniques we calculate analytically as wel…
We study the resonance fluorescence from a coherently driven four-level atom in the Y-type configuration. The effects of quantum interference induced by spontaneous emission on the fluorescence properties of the atom are investigated. It is found that the quantum interference resulting from cascade emission decays of the atom leads to a splitting of resonances in the excited level populations calculated as a function of light detuning. For some parameters, interference assisted enhancement of inner sidebands and narrowing of central peaks may also occur in the fluorescence spectrum. We present…
A numerical method of calculating the non-Markovian evolution of a driven atom radiating into a structured continuum is developed. The formal solution for the atomic reduced density matrix is written as a Markovian algorithm by introducing a set of additional, virtual density matrices which follow, to the level of approximation of the algorithm, all the possible trajectories of the photons in the electromagnetic field. The technique is perturbative in the sense that more virtual density matrices are required as the product of the effective memory time and the effective coupling strength become…
We study phase-dependent fluctuations of the resonance fluorescence of a single $Λ$-type three-level atom in the regime near coherent population trapping, i.e., alongside the two-photon detuning condition. To this end, we employ the method of conditional homodyne detection (CHD) which considers squeezing in the weak driving regime, and extends to non-Gaussian fluctuations for saturating and strong fields. In this framework, and using estimated parameter settings of the resonance fluorescence of a single trapped $^{138} \mathrm{Ba}^{+}$ ion, the light scattered from the probe transitions is fou…
Starting point is a given semigroup of completely positive maps on the 2 times 2 matrices. This semigroup describes the irreversible evolution of a decaying 2-level atom. Using the integral-sum kernel approach to quantum stochastic calculus we couple the 2-level atom to an environment, which in our case will be interpreted as the electromagnetic field. The irreversible time evolution of the 2-level atom then stems from the reversible time evolution of atom and field together. Mathematically speaking, we have constructed a Markov dilation of the semigroup. The next step is to drive the atom by …
We describe a simple experimental technique which allows to store a single Rubidium 87 atom in an optical dipole trap. Due to light-induced two-body collisions during the loading stage of the trap the maximum number of captured atoms is locked to one. This collisional blockade effect is confirmed by the observation of photon anti-bunching in the detected fluorescence light. The spectral properties of single photons emitted by the atom were studied with a narrow-band scanning cavity. We find that the atomic fluorescence spectrum is dominated by the spectral width of the exciting laser light fie…
In the framework of the signal processing approach to single-atom resonance fluorescence with spectral resolution, we diagrammatically derive an analytical formula for arbitrary-order spectral correlation functions of the scattered fields that pass through Fabry-Perot interferometers. Our general expression is then applied to study correlation signals in the limit of well separated spectral lines of the resonance fluorescence spectrum. In particular, we study the normalized second-order temporal intensity correlation functions in the case of the interferometers tuned to the components of the s…
We overcome the diffraction limit in fluorescence imaging of neutral atoms in a sparsely filled one-dimensional optical lattice. At a periodicity of 433 nm, we reliably infer the separation of two atoms down to nearest neighbors. We observe light induced losses of atoms occupying the same lattice site, while for atoms in adjacent lattice sites, no losses due to light induced interactions occur. Our method points towards characterization of correlated quantum states in optical lattice systems with filling factors of up to one atom per lattice site.
We study the spectra of emission of a system composed by an atom, tightly confined inside a high-finesse resonator, when the atom is driven by a laser and is at steady state of the cooling dynamics induced by laser and cavity field. In general, the spectrum of resonance fluorescence and the spectrum at the cavity output contain complementary information about the dynamics undergone by the system. In certain parameter regimes, quantum interference effects between the scattering processes induced by cavity and laser field lead to the selective suppression of features of the resonance fluorescenc…
We show that the resonance shifts in the fluorescence of a cold gas of rubidium atoms substantially differ from those of thermal atomic ensembles that obey the standard continuous medium electrodynamics. The analysis is based on large-scale microscopic numerical simulations and experimental measurements of the resonance shifts in a steady-state response in light propagation.
We demonstrate a superconducting artificial atom with strong unidirectional coupling to a microwave photonic waveguide. Our artificial atom is realized by coupling a transmon qubit to the waveguide at two spatially separated points with time-modulated interactions. Direction-sensitive interference arising from the parametric couplings in our scheme results in a non-reciprocal response, where we measure a forward/backward ratio of spontaneous emission exceeding 100. We verify the quantum nonlinear behavior of this artificial chiral atom by measuring the resonance fluorescence spectrum under a s…
Spontaneous emission spectra of two initially excited closely spaced identical atoms are very sensitive to the strength and the direction of the applied magnetic field. The relevant schemes are considered that ensure the determination of the mutual spatial orientation of the atoms and the distance between them by entirely optical means. A corresponding theoretical description is given accounting for the dipole-dipole interaction between the two atoms in the presence of a magnetic field and for polarizations of the quantum field interacting with magnetic sublevels of the two-atom system.
We analyze the temporal response of the fluorescence light that is emitted from a dense gas of cold atoms driven by a laser. When the average interatomic distance is smaller than the wavelength of the photons scattered by the atoms, the system exhibits strong dipolar interactions and collective dissipation. We solve the exact dynamics of small systems with different geometries and show how these collective features are manifest in the scattered light properties such as the photon emission rate, the power spectrum and the second-order correlation function. By calculating these quantities beyond…
Pioneering methods in recent optical lattice experiments allow to focus laser beams down to a spot size that is comparable to the lattice constant. Inspired by this achievement, we examine the resonance fluorescence spectra of two-level atoms positioned in adjacent lattice sites and compare the case where the laser hits only one atom (single site addressing) with cases where several atoms are illuminated. In contrast to the case where the laser hits several atoms, the spectrum for single site addressing is no longer symmetric around the laser frequency. The shape of the spectrum of fluorescent…
We experimentally investigate the fluorescence photon emission characteristics for single q-dots by using optical nanofibers. We demonstrate that single q-dots can be deposited along an optical nanofiber systematically and reproducibly with a precision of 5 μm. For single q-dots on an optical nanofiber, we measure the fluorescence photon numbers coupled into the nanofiber and the normalized photon correlations, by varying the excitation laser intensity. We estimate the fluorescence photon coupling efficiency into the nanofiber guided modes to be higher than 9.4\pm3%.
We discuss the statistics of emission of photons by a single atom or ion illuminated by a laser beam at the frequency of quasi-resonance between two energy levels, a situation that corresponds to real experiments. We extend this to the case of two laser beams resonant with the energy differences between two excited levels and the ground state (three level atom in V-configuration). We use a novel approach of this type of problem by considering Kolmogorov equation for the probability distribution of the atomic state which takes into account first the deterministic evolution of this state under t…
