States of an Ensemble of Two-Level Atoms with Reduced Quantum Uncertainty
Monika H. Schleier-Smith, Ian D. Leroux, Vladan Vuletić
备注：
Letter (4 pages, 3 figures) followed by Auxiliary Material (10 pages, 6 figures). Minor changes in presentation and analysis of data. Significant expansion of Auxiliary Material. Broken images fixed
发表信息：
M. H. Schleier-Smith, I. D. Leroux, and V. Vuletic, Phys. Rev. Lett. 104, 073604 (2010)
We generate entangled states of an ensemble of 5*10^4 rubidium-87 atoms by optical quantum nondemolition measurement. The resonator-enhanced measurement leaves the atomic ensemble, prepared in a superposition of hyperfine clock levels, in a squeezed spin state. By comparing the resulting reduction of quantum projection noise (up to 8.8(8) dB) with the concomitant reduction of coherence, we demonstrate a clock input state with spectroscopic sensitivity 3.0(8) dB beyond the standard quantum limit.
Geometrical structures of quantum mechanics provide us with new insightful results about the nature of quantum theory. In this work we consider mixed quantum states represented by finite rank density operators. We review our geometrical framework that provide the space of density operators with Riemannian and symplectic structures, and we derive a geometric uncertainty relation for observables acting on mixed quantum states. We also give an example that visualizes the geometric uncertainty relation for spin-$\frac{1}{2}$ particles.
Atomic clocks are typically operated by locking a local oscillator (LO) to a single atomic ensemble. In this article we propose a scheme where the LO is locked to several atomic ensembles instead of one. This results in an exponential improvement compared to the conventional method and provides a stability of the clock scaling as $(αN)^{-m/2}$ with $N$ being the number of atoms in each of the $m$ ensembles and $α$ is a constant depending on the protocol being used to lock the LO
We consider the optical generation and verification of entanglement in atomic ensembles under non-uniform interaction between the ensemble and an optical mode. We show that for a wide range of parameters a system of non-uniformly coupled atomic spins can be described as an ensemble of uniformly coupled spins with a reduced effective atom-light coupling and a reduced effective atom number, with a reduction factor of order unity given by the ensemble-mode geometry. This description is valid even for complex entangled states with arbitrary phase-space distribution functions as long as the detecti…
We propose a method to achieve quantum supremacy using ensembles of qubits, using only spin squeezing, basis rotations, and Fock state measurements. Each ensemble is assumed to be controllable only with its total spin. Using a repeated sequence of random basis rotations followed by squeezing, we show that the probability distribution of the final measurements quickly approaches a Porter-Thomas distribution. We show that the sampling probability can be related to a #P-hard problem with a complexity scaling as $(N+1)^M$, where $N$ is the number of qubits in an ensemble and $ M $ is the number of…
Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon
近年来，利用集体增强技术成功地实现了原子系综与单光子的纠缠[D. N. Matsukevich，\textit{et al.}，物理学评论快报。\textbf{95}，040405（2005）.]，其中原子内态和光子偏振态以非局域方式关联。在这里，我们通过实验阐明了在原子系综和光子系统中，也存在着与空间自由度有关的纠缠。讨论了远程原子系综之间高维纠缠的产生及其在凝聚态物理中的应用。
We propose to couple single atomic qubits to photons incident on a cavity containing an atomic ensemble of a different species that mediates the coupling via Rydberg interactions. Subject to a classical field and the cavity field, the ensemble forms a collective dark state which is resonant with the input photon, while excitation of a qubit atom leads to a secondary "dark" state that splits the cavity resonance. The two different dark state mechanisms yield zero and $π$ reflection phase shifts and can be used to implement quantum gates between atomic and optical qubits.
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 study the collective radiation properties of cold, trapped ensembles of atoms. We consider the high density regime with the mean interatomic distance being comparable to, or smaller than, the wavelength of the resonant optical radiation emitted by the atoms. We find that the emission rate of a photon from an excited atomic ensemble is strongly enhanced for an elongated cloud. We analyze collective single-excitation eigenstates of the atomic ensemble and find that the absorption/emission spectrum is broadened and shifted to lower frequencies as compared to the non-interacting (low density) o…
We present an analytic solution of bound states in the continuum (BICs) for photons and atoms in a one-dimensional coupled cavity array. These bound states are formed by two ensembles of twolevel atoms confined in separated cavities of the array. We show that in the regime where the photon hopping rate between neighboring cavities is high compared with the collective Rabi frequency, the BIC corresponds to a subradiant collective atomic state in which the two ensembles of atoms are strongly entangled. On the other hand in the low photon hopping rate regime, the BIC behaves a quantum cavity in w…
On quantum logic operations based on photon-exchange interactions in an ensemble of non-interacting atoms
最近提出的通过原子系综中的交换相互作用在光子态之间产生纠缠的想法（J.D. Franson和T. B. Pitman，Phys.Rev.A60，917（1999）和J.D. Franson等人，（quant-ph/9912121））使用S-matix方法进行讨论。结果表明，如果原子的非线性响应可以忽略，并且没有额外的原子-原子相互作用，交换作用在使原子返回到初始态的过程中不会产生光子态之间的纠缠.纠缠的产生需要存在非线性原子响应或原子-原子相互作用。
Atomic ensembles are effective memory nodes for quantum communication network due to the long coherence time and the collective enhancement effect for the nonlinear interaction between an ensemble and a photon. Here we investigate the possibility of achieving the entanglement distillation for nonlocal atomic ensembles by the input-output process of a single photon as a result of cavity quantum electrodynamics. We give an optimal entanglement concentration protocol (ECP) for two-atomic-ensemble systems in a partially entangled pure state with known parameters and an efficient ECP for the system…
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…
Two-bit Deutsch-Jozsa algorithm using an atomic ensemble
第一个实现二比特版本Deutsch-Jozsa算法的光学方案[D. Deutsch和R. Jozsa，Proc. R. Soc. London A { \bf 493}，553（1992）]。该提案在原子系综和简并光子源中使用斯塔克位移。光子与原子系综色散相互作用，导致原子-场基的有效哈密顿量，这对于执行所需的双量子比特操作是有用的。将这些与一组单量子比特操作相结合，可以实现该算法。给出了该建议的实验可行性的讨论。
We analyze the operation of a novel sensor based on atom interferometry, which can achieve supra-classical sensitivity by exploiting quantum correlations in mixed states of many qubits. The interferometer is based on quantum gates which use coherently-controlled Rydberg interactions between a single atom (which acts as a control qubit) and an atomic ensemble (which provides register qubits). In principle, our scheme can achieve precision scaling with the size of the ensemble - which can extend to large numbers of atoms - while using only single-qubit operations on the control and bulk operatio…
The generation and storage of entangled photons play important roles in quantum information technique. Spontaneous Raman scattering (SRS) in atomic ensembles provides a promising method to generate entangled photons capable of storage. In the past experiments, a spin-wave-photon entangled state is produced via SRS in an atomic ensemble, with which a pair of entangled photons is obtained. Here, we report a scheme of simultaneously generating two spin-wave-photon entangled states in an atomic ensemble by collecting Stokes photons at two different directions. Based on the obtained two atom-photon…
We demonstrate $|W\rangle$ state encoding of multi-atom ensemble qubits. Using optically trapped Rb atoms the $T_2$ coherence time is 2.6(3) ms for $\bar N=7.6$ atoms and scales approximately inversely with the number of atoms. Strong Rydberg blockade between two ensemble qubits is demonstrated with a fidelity of $0.89(1)$ and a fidelity of $\sim \hspace{-.05cm}1.0$ when postselected on control ensemble excitation. These results are a significant step towards deterministic entanglement of atomic ensembles.
We propose an efficient method to filter out single atoms from trapped ensembles with unknown number of atoms. The method employs stimulated adiabatic passage to reversibly transfer a single atom to the Rydberg state which blocks subsequent Rydberg excitation of all the other atoms within the ensemble. This triggers the excitation of Rydberg blockaded atoms to short lived intermediate states and their subsequent decay to untrapped states. Using an auxiliary microwave field to carefully engineer the dissipation, we obtain a nearly deterministic single-atom source. Our method is applicable to sm…
Rydberg atoms are at the core of an increasing number of experiments, which frequently rely on destructive detection methods, such as field ionization. Here, we present an experimental realization of single-shot non-destructive detection of ensembles of helium Rydberg atoms. We use the dispersive frequency shift of a superconducting microwave cavity interacting with the ensemble. By probing the transmission of the cavity and measuring the change in its phase, we determine the number of Rydberg atoms or the populations of Rydberg quantum states when the ensemble is prepared in a superposition. …
