We discuss the use of electromagnetically modified absorption to achieve selective excitation in atoms: that is, the laser excitation of one transition while avoiding simultaneously exciting another transition whose frequency is the same as or close to that of the first. The selectivity which can be achieved in the presence of electromagnetically induced transparency (EIT) is limited by the decoherence rate of the dark state. We present exact analytical expressions for this effect, and also physical models and approximate expressions which give useful insights into the phenomena. When the laser frequencies are near-resonant with the single-photon atomic transitions, EIT is essential for achieving discrimination. When the laser frequencies are far detuned, the `bright' two-photon Raman resonance is important for achieving selective excitation, while the `dark' resonance (EIT) need not be. The application to laser cooling of a trapped atom is also discussed.
We perform a quantum-theoretical treatment of cavity linewidth narrowing with intracavity electromagnetically induced transparency (EIT). By means of intracavity EIT, the photons in the cavity are in the form of cavity polaritons: bright-state polariton and dark-state polariton. Strong coupling of the bright-state polariton to the excited state induces an effect known as vacuum Rabi splitting, whereas the dark-state polariton decoupled from the excited state induce a narrow cavity transmission window. Our analysis would provide a quantum theory of linewidth narrowing with a quantum field pulse…
It is known that cross-correlation between the random intensity fluctuations of two lasers forming electromagnetically-induced transparency (EIT) exhibits a transition from correlation to anticorrelation. We study the linewidth behavior of this transition and have found the linewidth is below the (effective) coherence lifetime limit and is only limited by competing noises. We established a numerical model which reveals the linewidth dependence on laser linewidth and laser power. Our experiments using lasers with different linewidth showed results in qualitative agreement with the model. This r…
We analyze the two-photon linewidth of the recently proposed adiabatic transfer technique for ``stopping'' of light using electromagnetically induced transparency (EIT). We shown that a successful and reliable transfer of excitation from light to atoms and back can be achieved if the spectrum of the input probe pulse lies within the initial transparency window of EIT, and if the two-photon detuning $δ$ is less than the collective coupling strength (collective vacuum Rabi-frequency) $g\sqrt{N}$ divided by $\sqrt{γT}$, with $γ$ being the radiative decay rate, $N$ the effective number of atoms in…
Resonant dipole-dipole interaction (RDDI) is ubiquitous in light-matter interacting systems and is responsible for many fascinating properties of collective radiations. Here we theoretically investigate the role of RDDI in electromagnetically induced transparency (EIT). The resonant dipole-dipole interactions manifest in the cooperative spontaneous emission of the probe light transition, which give rise a broadened linewidth and associated collective frequency shift. This cooperative linewidth originates from the nonlocal and long-range RDDI, which can be determined by the atomic density, opti…
We address the problem of discriminating with minimal error probability two given quantum operations. We show that the use of entangled input states generally improves the discrimination. For Pauli channels we provide a complete comparison of the optimal strategies where either entangled or unentangled input states are used.
We report on the all-optical detection of Rydberg states in a effusive atomic beam of strontium atoms using electromagnetically induced transparency (EIT). Using narrow-linewidth CW lasers we obtain an EIT linewidth of 5 MHz. To illustrate the high spectroscopic resolution offered by this method, we have measured isotope shifts of the 5s18d ^1D_2 and 5s19s ^1S_0 Rydberg states. This technique could be applied to high-resolution, non-destructive measurements of ultra-cold Rydberg gases and plasmas.
We show how to optimally unambiguously discriminate between two subspaces of a Hilbert space. In particular we suppose that we are given a quantum system in either the state ψ_{1}, where ψ_{1} can be any state in the subspace S_{1}, or ψ_{2}, where ψ_{2} can be any state in the subspace S_{2}, and our task is to determine in which of the subspaces the state of our quantum system lies. We do not want to make a mistake, which means that our procedure will sometimes fail if the subspaces are not orthogonal. This is a special case of the unambiguous discrimination of mixed states. We present the P…
We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is unambiguous, i. e. error-free, discrimination with a minimum probability of getting an inconclusive outcome, where the measurement fails to give a definite answer. For distinguishing between two mixed quantum states, we investigate the relation between the minimum error probability achievable in conclusive discrimination, and the minimum failure probability that ca…
We report here the first observation of electromagnetically induced transparency (EIT) in $^{20}$Ne. The power broadening of the EIT linewidth is measured as a function of neon pressure and RF excitation power. Doppler effects on the EIT broadening are found even at low pressures and low intensities, where the linewidth should be governed only by homogeneous effects.
The problem of discriminating with minimum error between two mixed quantum states is reviewed, with emphasize on the detection operators necessary for performing the measurement. An analytical result is derived for the minimum probability of errors in deciding whether the state of a quantum system is either a given pure state or a uniform statistical mixture of any number of mutually orthogonal states. The result is applied to two-qubit states, and the minimum error probabilities achievable by collective and local measurements on the qubits are compared.
The problem of quantum state filtering consists of determining whether an unknown quantum state, which is chosen from a known set of states, is either a particular, specified state, or not. We consider this problem for the case that the filtering procedure is required to be unambiguous, which necessitates admitting inconclusive answers when the given states are not orthogonal. As an application, we propose an efficient, probabilistic procedure for distinguishing between sets of Boolean functions, which is an extension of the Deutsch-Jozsa algorithm.
We describe the generation of atom-resonant indistinguishable photon pairs using nonlinear optical techniques, their spectral purification using atomic filters, characterization using multi-photon interference, and application to quantum-enhanced sensing with atoms. Using either type-I or type-II cavity-enhanced spontaneous parametric down-conversion, we generate pairs of photons in the resonant modes of optical cavities with linewidths comparable to the 6 MHz natural linewidth of the D$_1$ line of atomic rubidium. The cavities and pump lasers are tuned so that emission occurs in a mode or a p…
We discuss the problem of implementing generalized measurements (POVMs) with linear optics, either based upon a static linear array or including conditional dynamics. In our approach, a given POVM shall be identified as a solution to an optimization problem for a chosen cost function. We formulate a general principle: the implementation is only possible if a linear-optics circuit exists for which the quantum mechanical optimum (minimum) is still attainable after dephasing the corresponding quantum states. The general principle enables us, for instance, to derive a set of necessary conditions f…
We discuss the following variant of the standard minimum error state discrimination problem: Alice picks the state she sends to Bob among one of several disjoint state ensembles, and she communicates him the chosen ensemble only at a later time. Two different scenarios then arise: either Bob is allowed to arrange his measurement set-up after Alice has announced him the chosen ensemble, or he is forced to perform the measurement before of Alice's announcement. In the latter case, he can only post-process his measurement outcome when Alice's extra information becomes available. We compare the op…
We utilized the all-copropagating scheme, which maintains the phase-match condition, in the spontaneous four-wave mixing (SFWM) process to generate biphotons from a hot atomic vapor. The scheme enables our biphotons not only to surpass those in the previous works of hot-atom SFWM, but also to compete with the biphotons that are generated by either the cold-atom SFWM or the cavity-assisted spontaneous parametric down conversion. The biphoton linewidth in this work is tunable for an order of magnitude. As we tuned the linewidth to 610 kHz, the maximum two-photon correlation function, $g_{s,as}^{…
A bipartite state which is secretly chosen from a finite set of known entangled pure states cannot be immediately useful in standard quantum information processing tasks. To effectively make use of the entanglement contained in this unknown state, we introduce a new way to locally manipulate the original quantum system: either identify the state successfully or distill some pure entanglement. Remarkably, if many copies are available, we show that any finite set of entangled pure states, whatever orthogonal or not, can be locally distinguished in this way, which further implies that pure entang…
We systematically studied the temporal profile of biphotons, i.e., pairs of time-correlated single photons, generated from a hot atomic vapor via the spontaneous four-wave mixing process. The measured temporal width of biphoton wave packet or two-photon correlation function against the coupling power was varied from about 70 to 580 ns. We derived an analytical expression of the biphoton's spectral profile in the Doppler-broadened medium. The analytical expression reveals that the spectral profile is mainly determined by the effect of electromagnetically induced transparency (EIT), and behaves …
We consider the Unambiguous State Discrimination (USD) of two mixed quantum states. We study the rank and the spectrum of the elements of an optimal USD measurement. This naturally leads to a partial fourth reduction theorem. This theorem shows that either the failure probability equals its overall lower bound given in term of the fidelity or a two-dimensional subspace can be split off from the original Hilbert space. We then use this partial reduction theorem to derive the optimal solution for any two equally probable Geometrically Uniform (GU) states $ρ_0$ and $ρ_1=Uρ_0 U^\dagger$, $U^2={\op…
Entangled states can help in quantum state discrimination by local operations and classical communication (LOCC). For example, a Bell state is necessary (and sufficient) to perfectly discriminate a set of either three or four Bell states by LOCC. In this paper, we consider the task of LOCC discrimination of the states of noisy Bell ensembles, where a given ensemble consists of the states obtained by mixing the Bell states with an arbitrary two-qubit state with nonzero probabilities. It is proved that a Bell state is required for optimal discrimination by LOCC, even though the ensembles do not …
Electromagnetically-induced transparency (EIT) exploits quantum coherence to burn subnatural linewidth holes within a spectral line. We investigate the less explored properties of EIT to effect absorptive nonlinear processes without restrictions on the relative intensities of pump and probe fields. We show that a three-level medium under imperfect EIT conditions can generate a form of bleaching that is qualitatively similar to two-state saturable absorption. This scheme has the advantages of greater sensitivity to signal intensity and controllability over its bleaching intensity level post-fab…
We report characterization of electromagnetically induced transparency (EIT) resonances in the D1 line of Rb-87 under various experimental conditions. The dependence of the EIT linewidth on the power of the pump field was investigated, at various temperatures, for the ground states of the lambda-system associated with different hyperfine levels of the atomic 5S_1/2 state as well as magnetic sublevels of the same hyperfine level. Strictly linear behavior was observed in all cases. A theoretical analysis of our results shows that dephasing in the ground state is the main source of decoherence, w…
We study the effects of frequency-dependent squeeze amplitude attenuation and squeeze angle rotation by electromagnetically induced transparency (EIT) on gravitational wave (GW) interferometers. We propose the use of low-pass, band-pass, and high-pass EIT filters, an S-shaped EIT filter, and an intra-cavity EIT filter to generate frequency-dependent squeezing for injection into the antisymmetric port of GW interferometers. We find that the EIT filters have several advantages over the previous filter designs with regard to optical losses, compactness, and the tunability of the filter linewidth.
High fidelity single shot qubit state readout is essential for many quantum information processing protocols. In superconducting quantum circuit, the qubit state is usually determined by detecting the dispersive frequency shift of a microwave cavity from either transmission or reflection. In this paper, we demonstrate the use of constructive interference between the transmitted and reflected signal to optimize the qubit state readout, with which we find a better resolved state discrimination and an improved qubit readout fidelity. As a simple and convenient approach, our scheme can be combined…
Electromagnetically-induced transparency (EIT) has been proposed as a way to greatly enhance cross-phase modulation, with the possibility of leading to few-photon-level optical nonlinearities. This enhancement grows as the transparency window width, Δ_EIT, is narrowed. Decreasing Δ_EIT, however, increases the response time of the effect, suggesting that for pulses of a given duration, there could be a fundamental limit to the strength of the nonlinearity. We show that in the regimes of most practical interest - narrow EIT windows perturbed by short signal pulses- the enhancement offered by EIT…
We consider the sequential quantum channel discrimination problem using adaptive and non-adaptive strategies. In this setting the number of uses of the underlying quantum channel is not fixed but a random variable that is either bounded in expectation or with high probability. We show that both types of error probabilities decrease to zero exponentially fast and, when using adaptive strategies, the rates are characterized by the measured relative entropy between two quantum channels, yielding a strictly larger region than that achievable by non-adaptive strategies. Allowing for quantum memory,…
The prevalent modus operandi within the framework of quantum resource theories has been to characterise and harness the resources within single objects, in what we can call \emph{single-object} quantum resource theories. One can wonder however, whether the resources contained within multiple different types of objects, now in a \emph{multi-object} quantum resource theory, can simultaneously be exploited for the benefit of an operational task. In this work, we introduce examples of such multi-object operational tasks in the form of subchannel discrimination and subchannel exclusion games, in wh…
Single atom imaging requires discrimination of weak photon count events above background and has typically been performed using either EMCCD cameras, photomultiplier tubes or single photon counting modules. sCMOS provides a cost effective and highly scalable alternative to other single atom imaging technologies, offering fast readout and larger sensor dimensions. We demonstrate single atom resolved imaging of two site-addressable single atom traps separated by 10~$μ$m using an sCMOS camera, offering a competitive signal-to-noise ratio at intermediate count rates to allow high fidelity readout …
In quantum state discrimination, the observers are given a quantum system and aim to verify its state from the two or more possible target states. In the local quantum state marking as an extension of quantum state discrimination, there are N composite quantum systems and N possible orthogonal target quantum states. Distant Alice and Bob are asked to correctly mark the states of the given quantum systems via local operations and classical communication. Here we investigate the local state marking with N 4 ${\otimes}$ 4 systems, N=4, 5, 6, and 7. Therein, Alice and Bob allow for three local ope…
We study, theoretically and experimentally, electromagnetically induced transparency (EIT) in two different solid-state systems. Unlike many implementations in homogeneously broadened media, these systems exhibit inhomogeneous broadening of their optical and spin transitions typical of solid-state materials. We observe EIT lineshapes typical of atomic gases, including a crossover into the regime of Autler-Townes splitting, but with the substitution of the inhomogeneous widths for the homogeneous values. We obtain quantitative agreement between experiment and theory for the width of the transpa…
We demonstrate laser frequency stabilization to excited state transitions using cascade electromagnetically induced transparency (EIT). Using a room temperature Rb vapor cell as a reference, we stabilize a first diode laser to the D2 transition and a second laser to a transition from the intermediate state to a Rydberg state with principal quantum number n=19 - 70. A combined laser linewidth of 280 kHz over a 0.1 ms time period is achieved. This method may be applied generally to any cascade system and allows laser stabilization to an atomic reference in the absence of strong optical transitio…
Pusan National University（釜山国立大学）；Quantum Sensors Research Center（量子传感器研究中心）；Quantum Science Technology Center, Pusan National University（釜山国立大学量子科学与技术中心）
Phase-Sensitive Heterodyne Detection of MW using EIT Harmonics in Rydberg Atoms
Johns Hopkins University（约翰斯·霍普金斯大学）；Indian Institute of Science（印度科学学院）；Defence Institute of Advanced Technology (Deemed University)（国防先进技术研究所（认定大学））；University of Bristol（布里斯托大学）；Indian Institute of Technology Guwahati（印度理工学院古瓦哈提分校）
Electromagnetically induced transparency (EIT) is a well-known phenomenon due in part to its applicability to quantum devices such as quantum memories and quantum gates. EIT is commonly modeled with a three-level lambda system due to the simplicity of the calculations. However, this simplified model does not capture all the physics of EIT experiments with real atoms. We present a theoretical study of the effect of two closely-spaced excited states on EIT and off-resonance Raman transitions. We find that the coherent interaction of the fields with two excited states whose separation is smaller …
We study electromagnetically induced transparency (EIT) of a weakly interacting cold Rydberg gas. We show that the onset of interactions is manifest as a depopulation of the Rydberg state and numerically model this effect by adding a density-dependent non-linear term to the optical Bloch equations. In the limit of a weak probe where the depopulation effect is negligible, we observe no evidence of interaction induced decoherence and obtain a narrow Rydberg dark resonance with a linewidth of <600 kHz, limited by the Rabi frequency of the coupling beam
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；RWTH Aachen University（亚琛工业大学）；City University of Hong Kong (Dongguan)（香港城市大学（东莞））；National Taiwan University（台湾大学）；National Center for Theoretical Sciences（国家理论科学中心）；Hon Hai (Foxconn) Quantum Computing Center（鸿海（富士康）量子计算中心）；Wuhan University（武汉大学）；Wuhan Institute of Quantum Science and Technology（武汉量子技术研究院）；International Quantum Academy（国际量子学院）；Nagoya University（名古屋大学）
We report the first observation of electromagnetically induced transparency (EIT) in an isotopically purified Nd$^{3+}$:YLiF$_4$ crystal. This crystal demonstrates inhomogeneous broadening of optical transitions of about 35 MHz. EIT is observed in a symmetrical $Λ$-like system formed by two hyperfine sublevels of the ground state corresponding to a zero first order Zeeman (ZEFOZ) transition and a hyperfine sublevel of the excited state, which is not coupled to other ground-state sublevels. It is found that transmission of the probe field as a function of the two-photon detuning demonstrates a …
The correlation spectroscopy has been successfully employed in the measurement of the intrinsic linewidth of electromagnetically induced transparency (EIT) in time and frequency domain. We study the role of the sidebands of the intense fields in the measured spectra, analyzing the information that can be recovered working with different analysis frequencies. In this case, the non-zero one-photon detuning appears as a necessary condition for spectrally resolving the sideband resonances in the correlation coefficient. Our experimental findings are supported by the perturbative model defined in t…
We use electromagnetically-induced transparency (EIT) to probe the narrow electron-spin resonance of nitrogen-vacancy centers in diamond. Working with a multi-pass diamond chip at temperatures 6-30 K, the zero-phonon absorption line (637 nm) exhibits an optical depth of 6 and inhomogenous linewidth of ~30 GHz full-width-at-half-maximum (FWHM). Simultaneous optical excitation at two frequencies separated by the ground-state zero-field splitting (2.88 GHz), reveals EIT resonances with a contrast exceeding 6% and FWHM down to 0.4 MHz. The resonances provide an all-optical probe of external electr…
