Gerhard C. Hegerfeldt
Modern techniques allow experiments on a single atom or system, with new phenomena and new challenges for the theoretician. We discuss what quantum mechanics has to say about a single system. The quantum jump approach as well as the role of quantum trajectories are outlined and a rather sophisticated example is given.
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Random Quantum States are presently of interest in the fields of quantum information theory and quantum chaos. Moreover, a detailed study of their properties can shed light on some foundational issues of the quantum statistical mechanics such as the emergence of well defined thermal properties from the pure quantum mechanical description of large many body systems. When dealing with an ensemble of pure quantum states, two questions naturally arise: what is the probability density function on the parameters which specify the state of the system in a given ensemble? And, does there exist a most …
We present and compare two families of ensembles of random density matrices. The first, static ensemble, is obtained foliating an unbiased ensemble of density matrices. As criterion we use fixed purity as the simplest example of a useful convex function. The second, dynamic ensemble, is inspired in random matrix models for decoherence where one evolves a separable pure state with a random Hamiltonian until a given value of purity in the central system is achieved. Several families of Hamiltonians, adequate for different physical situations, are studied. We focus on a two qubit central system, …
Minimal-error quantum state discrimination versus robustness of entanglement:More indistinguishability with less entanglement
本文研究了量子态鉴别与纠缠鲁棒性之间的关系，发现更少纠缠可带来更多不可区分性，并通过数值实验验证了相关边界条件。
The accessible information acc(E) of an ensemble E is the maximum mutual information between a random variable encoded into quantum states, and the probabilistic outcome of a quantum measurement of the encoding. Accessible information is extremely difficult to characterize analytically; even bounds on it are hard to place. The celebrated Holevo bound states that accessible information cannot exceed chi(E), the quantum mutual information between the random variable and its encoding. However, for general ensembles, the gap between the acc(E) and chi(E) may be arbitrarily large. We consider the s…
In this paper, we introduce an optical analogy to quantum Fourier tanformation based on a pseudorandom phase ensemble. The optical analogy also brings about exponential speedup over classical Fourier tanformation. Using the analogy, we demonstrate three classcial fields to realize Fourier transform similar to three quantum particles.
We study how to efficiently manipulate and store quantum information between optical fields and atomic ensembles. We show how various non-dissipative transfer schemes can be used to transfer and store quantum states such as squeezed vacuum states or entangled states into the long-lived ground state spins of atomic ensembles.
A novel method of multi-bit quantum optical data storage is presented, where the storage time can be lengthened far beyond the spin phase-decay time in a reversible spin inhomogeneous system excited by consecutive resonant Raman optical data pulses. The ultralong storage time is obtained by an optical population locking mechanism of modified rephasing process. This gives potentials to quantum repeaters utilizing quantum memories for long distance quantum communications, in which ultralong storage time plays a major role.
Scalable and efficient quantum computation with photonic qubits requires (i) deterministic sources of single-photons, (ii) giant nonlinearities capable of entangling pairs of photons, and (iii) reliable single-photon detectors. In addition, an optical quantum computer would need a robust reversible photon storage devise. Here we discuss several related techniques, based on the coherent manipulation of atomic ensembles in the regime of electromagnetically induced transparency, that are capable of implementing all of the above prerequisites for deterministic optical quantum computation with sing…
We study the atom-photon quantum interface with intracavity Rydberg-blocked atomic ensemble where the ground-Rydberg transition is realized by two-photon transition. Via theoretical analysis, we report our recent findings of the Jaynes-Cummings model on optical domain and robust atom-photon quantum gate enabled by this platform. The requirement on the implementation is mild which includes an optical cavity of moderately high finesse, typical alkali atoms such as Rb or Cs and the condition that cold atomic ensemble is well within the Rydberg blockade radius. The analysis focuses on the atomic e…
Long-lived quantum memories are essential components of a long-standing goal of remote distribution of entanglement in quantum networks. These can be realized by storing the quantum states of light as single-spin excitations in atomic ensembles. However, spin states are often subjected to different dephasing processes that limit the storage time, which in principle could be overcome using spin-echo techniques. Theoretical studies have suggested this to be challenging due to unavoidable spontaneous emission noise in ensemble-based quantum memories. Here we demonstrate spin-echo manipulation of …
We study the optical properties of an ensemble of two-level atoms coupled to a 1D photonic crystal waveguide (PCW), which mediates long-range coherent dipole-dipole interactions between the atoms. We show that the long-range interactions can dramatically alter the linear and nonlinear optical behavior, as compared to a typical atomic ensemble. In particular, in the linear regime, we find that the transmission spectrum reveals multiple transmission dips, whose properties we show how to characterize. In the many-photon regime the system response can be highly non-linear, and under certain circum…
Trapped atomic ensembles are convenient systems for quantum information storage in the long-lived sublevels of the electronic ground state and its conversion to propagating optical photons via stimulated Raman processes. Here we investigate a phase-matched emission of photons from a coherently prepared atomic ensemble. We consider an ensemble of cold atoms in an elongated harmonic trap with normal density distribution, and determine the parameters of paraxial optics to match the mode geometry of the emitted radiation and optimally collect it into an optical waveguide.
We review a series of quantum memory protocols designed to store the quantum information carried by light into atomic ensembles. In particular, we show how a simple semiclassical formalism allows to gain insight into various memory protocols and to highlight strong analogies between them. These analogies naturally lead to a classification of light storage protocols into two categories, namely photon echo and slow-light memories. We focus on the storage and retrieval dynamics as a key step to map the optical information into the atomic excitation. We finally review various criteria adapted for …
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 clarify the controversy over the coherent-state (CS) versus the number-state (NS) pictures in quantum optics. The NS picture is equivalent to the CS picture, as long as the phases $ϕ$ in the laser fields are randomly distributed, as Mølmer argues [\pra {\bf 55}, 3195 (1997)]. However, the claim by Rudolph and Sanders [Phys. Rev. Lett. {\bf 87}, 077903 (2001)] has a few gaps. First, they make an assumption that is not necessarily true in the calculation of a density operator involved with a two-mode squeezed state. We show that there exists entanglement in the density operator without defyin…
In the last few years there has been a lot of interest in quantum repeater protocols using only atomic ensembles and linear optics. Here we show that the local generation of high-fidelity entangled pairs of atomic excitations, in combination with the use of two-photon detections for long-distance entanglement generation, permits the implementation of a very attractive quantum repeater protocol. Such a repeater is robust with respect to phase fluctuations in the transmission channels, and at the same time achieves higher entanglement generation rates than other protocols using the same ingredie…
All-optical feedback can be effected by putting the output of a source cavity through a Faraday isolator and into a second cavity which is coupled to the source cavity by a nonlinear crystal. If the driven cavity is heavily damped, then it can be adiabatically eliminated and a master equation or quantum Langevin equation derived for the first cavity alone. This is done for an input bath in an arbitrary state, and for an arbitrary nonlinear coupling. If the intercavity coupling involves only the intensity (or one quadrature) of the driven cavity, then the effect on the source cavity is identica…
Many effects in the interaction between atoms and a cavity that are usually de-scribed in quantum mechanical terms (cavity quantum electrodynamics, cavity QED) can be understood and quantitatively analyzed within a classical framework. We adopt such a classical picture of a radiating dipole oscillator to derive explicit ex- pressions for the coupling of single atoms and atomic ensembles to Gaussian modes in free space and in an optical resonator. The cooperativity parameter of cavity QED is shown to play a central role, and is given a geometrical interpretation. The classical analysis yields t…
We consider a new approach for storing quantum information by macroscopic atomic excitations of two level atomic system. We offer the original scheme of quantum cloning of optical field into the cavity polaritons containing the phase insensitive parametrical amplifier and atomic cell placed in the cavity. The high temperature quasi-condensation (and/or condensation) phenomenon for polaritons arising in the cavity under the certain conditions is proposed for the first time.
We systematically study the interaction between two quantized optical fields and a cyclic atomic ensemble driven by a classic optical field. This so-called atomic cyclic ensemble consists of three-level atoms with Delta-type transitions due to the symmetry breaking, which can also be implemented in the superconducting quantum circuit by Yu-xi Liu et al. [Phys. Rev. Lett. 95, 087001 (2005)]. We explore the dynamic mechanisms to creating the quantum entanglements among photon states, and between photons and atomic collective excitations by the coherent manipulation of the atom-photon system. It …
We compare the accuracy, precision and reliability of different methods for estimating key system parameters for two-level systems subject to Hamiltonian evolution and decoherence. It is demonstrated that the use of Bayesian modelling and maximum likelihood estimation is superior to common techniques based on Fourier analysis. Even for simple two-parameter estimation problems, the Bayesian approach yields higher accuracy and precision for the parameter estimates obtained. It requires less data, is more flexible in dealing with different model systems, can deal better with uncertainty in initia…
We observe and measure dispersive optical non-linearities in an ensemble of cold Rydberg atoms placed inside an optical cavity. The experimental results are in agreement with a simple model where the optical non-linearities are due to the progressive appearance of a Rydberg blockaded volume within the medium. The measurements allow a direct estimation of the "blockaded fraction" of atoms within the atomic ensemble.
The interplay between classical and quantum mechanical evolution in the optical centrifuge (OC) is discussed. The analysis is based on the quantum mechanical formalism starting from either the ground state or a thermal ensemble. Two resonant mechanisms are identified, i.e. the classical autoresonance and the quantum mechanical ladder-climbing, yielding different dynamics and rotational excitation efficiencies. The rotating wave approximation is used to analyze the two resonant regimes in the associated dimensionless two-parameter space and calculate the OC excitation efficiency. The results sh…
We discuss a technique and a material system that enable the controlled realization of quantum entanglement between spin-wave modes of electron ensembles in two spatially separated pieces of semiconductor material. The approach uses electron ensembles in GaAs quantum wells that are located inside optical waveguides. Bringing the electron ensembles in a quantum Hall state gives selection rules for optical transitions across the gap that can selectively address the two electron spin states. Long-lived superpositions of these electron spin states can then be controlled with a pair of optical fiel…
An analytical prediction is established of how an isolated many-body quantum system relaxes towards its thermal long-time limit under the action of a time-independent perturbation, but still remaining sufficiently close to a reference case whose temporal relaxation is known. This is achieved within the conceptual framework of a typicality approach by showing and exploiting that the time-dependent expectation values behave very similarly for most members of a suitably chosen ensemble of perturbations. The predictions are validated by comparison with various numerical and experimental results fr…
We propose a theoretical model which describes the coupling between quantum dots ensemble and optical microcavity. By this model we simulate the interaction of the system with the strain pulse which can strongly modify the lasing of QDs.
We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of Caldeira-Leggett type, where the collective coordinate is coupled to an internal bath of phonons. In contrast to the usual Caldeira-Leggett model, the bath in the present case is part of the system. We derive an equation of motion for the collective coordinate which takes the form of a damped harmonic oscillator. We show that the distribution of quantum transi…
We propose a realization of two remarkable effects of Dicke physics in quantum simulation of light-matter many-body interactions with artificial quantum systems. These effects are a superradiant decay of an ensemble of qubits and the opposite radiation trapping effect. We show that both phenomena coexist in the crossover regime of a "moderately bad" single-mode cavity coupled to the qubit subsystem. Depending on the type of the initial state and on the presence of multipartite entanglement in it, the dynamical features can be opposite resulting either in the superradiance or in the radiation t…
Recent experiments have shown that (quasi-)crystalline phases of Rydberg-dressed quantum many-body systems in optical lattices (OL) are within reach. Rydberg systems naturally possess strong long-range interactions due to the large polarizability of Rydberg atoms. Thus a wide range of quantum phases have been predicted, such as a devil's staircase of lattice incommensurate density wave phases as well as more exotic lattice supersolid order for bosonic systems, as considered in our work. Guided by results in the "frozen" gas limit, we study the ground state phase diagram at finite hopping ampli…
Ensembles of erbium dopants can realize quantum memories and frequency converters that operate in the minimal-loss wavelength band of fiber optical communication. Their operation requires the initialization, coherent control and readout of the electronic spin state. In this work, we use a split-ring microwave resonator to demonstrate such control in both the ground and optically excited state. The presented techniques can also be applied to other combinations of dopant and host, and may facilitate the development of new quantum memory protocols and sensing schemes.
We provide a comprehensive study of atomic Raman and Bragg diffraction when coupling to a pair of counterpropagating light gratings (double diffraction) or to a single one (single diffraction) and discuss the transition from one case to the other in a retroreflective geometry as the Doppler detuning changes. In contrast to single diffraction, double Raman loses its advantage of high diffraction efficiency for short pulses and has to be performed in a Bragg-type regime. Moreover, the structure of double diffraction leads to further limitations for broad momentum distributions on the efficiency …
Structures of quantum Fokker-Planck equations are characterized with respect to the properties of complete positivity, covariance under symmetry transformations and satisfaction of equipartition, referring to recent mathematical work on structures of unbounded generators of covariant quantum dynamical semigroups. In particular the quantum optical master-equation and the quantum Brownian motion master-equation are shown to be associated to $\mathrm{U(1)}$ and $\mathrm{R}$ symmetry respectively. Considering the motion of a Brownian particle, where the expression of the quantum Fokker-Planck equa…
Motivated by the anisotropic long-range nature of the interactions between cold dipolar atoms or molecules in an optical lattice, we study the anisotropic quantum Heisenberg model with Curie-Weiss-type long-range interactions. Absence of a heat bath in optical lattice experiments suggests a study of this model within the microcanonical ensemble. The microcanonical entropy is calculated analytically, and nonequivalence of microcanonical and canonical ensembles is found for a range of anisotropy parameters. From the shape of the entropy it follows that the Curie-Weiss Heisenberg model is indisti…
Atomic ensembles have many potential applications in quantum information science. Owing to collective enhancement, working with ensembles at high densities increases the overall efficiency of quantum operations, but at the same time also increases the collision rate and leads to faster decoherence. Here we report on experiments with optically trapped 87Rb atoms demonstrating a 20-fold increase of the coherence time when a dynamical decoupling sequence with more than 200 pi-pulses is applied. We perform quantum process tomography and demonstrate that using the decoupling scheme a dense ensemble…
Optical lattice clocks can now resolve the height difference below 1 mm within an atomic ensemble by means of gravitational redshift with integration over sufficient amount of time. Further improvement in the stability enables the clocks to resolve the height difference of subsystems within an atomic ensemble that is conventionally interrogated as a single coherent spin state in a single Ramsey sequence, resulting in the dephasing of the coherent spin state. This effect is observable with a clock of a stability of $\lesssim 10^{-21}$ by introducing a single-layer-resolved imaging system for a …
Different ensembles of quantum states can have the same average nonpure state. Distinguishing between such constructions, via different mixing procedures of the same nonpure quantum state, is known to entail signaling. In parallel, different superpositions of pure quantum states can lead to the same pure state. We show that the possibility of distinguishing between such preparations, via different interferometric setups leading to the same pure quantum state, also implies signaling. The implication holds irrespective of whether the distinguishing procedure is deterministic or probabilistic.
We use optical tweezers based on time-multiplexed acousto-optic deflectors to trap ultra-cold cesium atoms in one-dimensional arrays of atomic ensembles. For temperatures between 2.5 $μ$K and 50 nK we study the maximal time between optical tweezer pulses that retains the number of atoms in a single trap. This time provides an estimate on the maximal number of sites in an array of time-multiplexed optical tweezers. We demonstrate evaporative cooling of atoms in arrays of up to 25 optical tweezer traps and the preparation of atoms in a box potential. Additionally, we demonstrate three different …
We discuss the evolution of the quantum state of an ensemble of atoms that are coupled via a single propagating optical mode. We theoretically show that the quantum state of N atoms, which are initially prepared in the timed Dicke state, evolves through all the N - 1 states that are subradiant with respect to the propagating mode. We predict this process to occur for any atom number and any atom-light coupling strength. These findings are supported by measurements performed with cold cesium atoms coupled to the evanescent field of an optical nanofiber. We experimentally observe the evolution o…
We examine quantum statistics of optical photons emitted from atomic ensembles which are classically driven and simultaneously coupled to a two-level atom via microwave photon exchange. Quantum statistics and correlations are analyzed by calculating second order coherence degree, von Neumann entropy, spin squeezing for multi-particle entanglement, as well as genuine two and three-mode entanglement parameters for steady state and non-equilibrium situations. Coherent transfer of population between the radiation modes and quantum state mapping between the two-level atom and the optical modes are …
Single-Atomic-Ensemble Dual-Wavelength Optical Standard
本研究基于铷原子系综的双光学跃迁调制转移光谱技术，实现单蒸汽池内780nm与795nm激光器的同时稳定，频率不稳定性达10^(-14)低量级，可拓展至多波长光学频率标准应用。
Reducing the instability of an optical lattice clock using multiple atomic ensembles
本文通过多原子系综的相位估计方法，在锶光晶格钟中实现不稳定性降低2.08倍，并增强相干询问时间3倍以上。
Lattice Light Shift Evaluations In a Dual-Ensemble Yb Optical Lattice Clock
针对光晶格钟中超电偶极极化率导致魔法波长囚禁失效、多极极化率项实验与理论存在差异的问题，提出结合成像与多系综技术、利用双系综镱光晶格钟快速评估差分频移，并采用行波场探测两类极化率系数的新方法。
Atomic interferometry in optical lattices is a new trend of developing practical quantum gravimeter. Here, we propose a compact and portable gravimetry scheme with an ensemble of ultracold atoms in gravitationally tilted spin-dependent optical lattices. The fast, coherent separation and recombination of atoms can be realized via polarization-synthesized optical lattices. The input atomic wavepacket is coherently split into two parts by a spin-dependent shift and a subsequent $\fracπ{2}$ pulse. Then the two parts are held for accumulating a relative phase related to the gravity. Lastly the two …
Statistical ensemble formalism of Kim, Mandel and Wolf (J. Opt. Soc. Am. A 4, 433 (1987)) offers a realistic model for characterizing the effect of stochastic non-image forming optical media on the state of polarization of transmittedlight. With suitable choice of the Jones ensemble, various Mueller transformations - some of which have been unknown so far - are deduced. It is observed that the ensemble approach is formally identical to the positive operator valued measures (POVM) on the quantum density matrix. This observation, in combination with the recent suggestion by Ahnert and Payne (Phy…
Spins bound to point defects are increasingly viewed as an important resource for solid-state implementations of quantum information technologies. In particular, there is a growing interest in the identification of new classes of defect spin that can be controlled optically. Here we demonstrate ensemble optical spin polarization and optically detected magnetic resonance (ODMR) of the S = 1 electronic ground state of chromium (Cr4+) impurities in silicon carbide (SiC) and gallium nitride (GaN). Spin polarization is made possible by the narrow optical linewidths of these ensembles (< 8.5 GHz), w…
The influence of evanescent waves on the nature of optical cooperative effects in atomic ensembles in a waveguide
研究倏逝波对原子团块中集体多原子效应的影响，揭示其对协同自发辐射过程和辐射传输性质的改变机制。
We present programmable two-dimensional arrays of microscopic atomic ensembles consisting of more than 400 sites with nearly uniform filling and small atom number fluctuations. Our approach involves direct projection of light patterns from a digital micromirror device with high spatial resolution onto an optical pancake trap acting as a reservoir. This makes it possible to load large arrays of tweezers in a single step with high occupation numbers and low power requirements per tweezer. Each atomic ensemble is confined to $\sim 1\,μ$m$^3$ with a controllable occupation from 20 to 200 atoms and…
We study the effects of high optical depth and density on the performance of a light-atom quantum interface. An in-situ imaging method, a dual-port polarization contrast technique, is presented. This technique is able to compensate for image distortions due to refraction. We propose our imaging method as a tool to characterize atomic ensembles for high capacity spatial multimode quantum memories. Ultracold dense inhomogeneous Rubidium samples are imaged and we find a resonant optical depth as high as 680 on the D1 line. The measurements are compared with light-atom interaction models based on …
Unlocking n-alk-1-ynes Conformers: Quantum "Trigger Finger" versus "Stiff Joint" Conformations
本研究通过量子化学分析揭示了 n-alk-1-ynes 炔端存在平面与倾斜两种近乎等能的构象，阐明了其独特的量子“扳机指”动力学特征，为分子电子学中的光谱数据解释与构象控制提供了新蓝图。
We propose to use molecular picocavity ensembles as macroscopic coherent nonlinear optical devices enabled by nanoscale strong coupling. For a generic picocavity model that includes molecular and photonic disorder, we derive theoretical performance bounds for coherent cross-phase modulation signals using weak classical fields of different frequencies. We show that strong coupling of the picocavity {\it vacua} with a specific vibronic sideband in the molecular emission spectrum results in a significant variation of the effective refractive index of the metamaterial relative to a molecule-free s…
Defect-based quantum emitters in solid state materials offer a promising platform for quantum communication and sensing. Confocal fluorescence microscopy techniques have revealed quantum emitters in a multitude of host materials. In some materials, however, optical properties vary widely between emitters, even within the same sample. In these cases, traditional ensemble fluorescence measurements are confounded by heterogeneity, whereas individual defect-by-defect studies are impractical. Here, we develop a method to quantitatively and systematically analyze the properties of heterogeneous emit…
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