Macroscopic Coherence for a Trapped Electron

Detecting macroscopic quantum coherence with a cavity optomechanical system

The rigorous resource framework of quantum coherence has been set up recently and excited a wide variety of interests. Here we show that a quantum cavity optomechanical system, as an emerging platform, can behave with a certain value of quantum coherence at a macroscopic scale. We also find that the difference between the total optomechanical coherence and the sum of the optical and the mechanical coherence just equals their mutual information. Motivated by the detection of the optomechanical entanglement, an experimentally feasible scheme to probe the optomechanical coherence is proposed.

Coherence Based Characterization of Macroscopic Quantumness

One of the most elusive problems in quantum mechanics is the transition between classical and quantum physics. This problem can be traced back to the Schrödinger's cat. A key element that lies at the center of this problem is the lack of a clear understanding and characterization of macroscopic quantum states. Our understanding of Macroscopic Quantumness relies on states such as the Greenberger-Horne-Zeilinger(GHZ) or the NOON state. Here we take a first principle approach to this problem. We start from coherence as the key quantity that captures the notion of quantumness and demand the quantu…

Disturbance-Based Measure of Macroscopic Coherence

We propose a measure of macroscopic coherence based on the degree of disturbance caused by a coarse-grained measurement. Based on our measure, we point out that recently proposed criteria of macroscopic coherence may lead to inconsistent results when considering certain states such as a product of microscopic superpositions. An inequality relation is proved that relates the Wigner-Yanase-Dyson skew information and the measurement disturbance, providing arguments as to why our approach is able to rule out such inconsistencies. We show that our measure can also quantify the fragility of a quantu…

Qubit Assisted Probing of Coherence Between States of a Macroscopic Apparatus

I present a general scheme through which the evidence of a superposition involving distinct classical-like states of a macroscopic system can be probed. The scheme relies on a qubit being coupled to a macroscopic harmonic oscillator in such a way that it can be used to both prepare and probe a macroscopic superposition. Two potentially realizable implementations, one with a flux qubit coupled to a LC circuit, and the other with an ion-trap qubit coupled to the collective motion of several ions, are proposed.

Ponderomotive Control of Quantum Macroscopic Coherence

It is shown that because of the radiation pressure a Schrödinger cat state can be generated in a resonator with oscillating wall. The optomechanical control of quantum macroscopic coherence and its detection is taken into account introducing new cat states. The effects due to the environmental couplings with this nonlinear system are considered developing an operator perturbation procedure to solve the master equation for the field mode density operator.

具有多秒相干性的腔界面囚禁离子量子比特寄存器

A Cavity-Interfaced Register of Trapped-Ion Qubits with Multi-Second Coherence

本研究在腔集成离子阱中实现了5个共囚禁离子量子比特的多秒相干性，验证了离子-光子纠缠的多秒存储能力，为构建多量子比特囚禁离子量子处理器网络奠定了基础。

Certifying Multilevel Coherence in the Motional State of a Trapped Ion

Quantum coherence is one of the clearest departures from classical physics, exhibited when a system is in a superposition of different basis states. Here the coherent superposition of three motional Fock states of a single trapped ion is experimentally certified, with a procedure provably robust against imperfect operation. As the motional state cannot be directly interrogated, our scheme uses an interference pattern generated by projective measurement of the coupled qubit state. The minimum number of coherently superposed states is inferred from a series of threshold values based on analysis …

Coherence of a qubit stored in Zeeman levels of a single optically trapped atom

We experimentally investigate the coherence properties of a qubit stored in the Zeeman substates of the 5S1/2, F=1 hyperfine ground level of a single optically trapped Rb-87 atom. Larmor precession of a single atomic spin-1 system is observed by preparing the atom in a defined initial spin-state and then measuring the resulting state after a programmable period of free evolution. Additionally, by performing quantum state tomography, maximum knowledge about the spin coherence is gathered. By using an active magnetic field stabilization and without application of a magnetic guiding field we achi…

Experimental macroscopic coherence by phase-covariant cloning of a single photon

We investigate the multiphoton states generated by high-gain optical parametric amplification of a single injected photon, polarization encoded as a ''qubit''. The experiment configuration exploits the optimal phase-covariant cloning in the high gain regime. The interference fringe pattern showing the non local transfer of coherence between the injected qubit and the mesoscopic amplified output field involving up to 4000 photons has been investigated. A probabilistic new method to extract full information about the multiparticle output wavefunction has been implemented.

机械系统中的宏观量子相干与纠缠

Macroscopic quantum coherence and entanglement in mechanical systems

本文提出广延尺度和纠缠尺度两种度量，从量子相干与多体纠缠角度统一刻画宏观量子性，并利用微机械振荡器与分子衍射实验数据验证，发现10^6至10^7个原子的真正多体纠缠。

Stability of spherically trapped three-dimensional Bose-Einstein condensates against macroscopic fragmentation

We consider spherically trapped Bose gases in three dimensions with contact interactions, and investigate whether the Bose-Einstein condensate at zero temperature is stable against macroscopic fragmentation into a small number of mutually incoherent pieces. Our results are expressed in terms of a dimensionless interaction measure proportional to the Thomas-Fermi parameter. It is shown that while three-dimensional condensates are inherently much more stable against macroscopic fragmentation than their quasi-one- and quasi-two-dimensional counterparts, they fragment at a sufficiently large value…

超越十小时的相干性在去相干自由的囚禁离子钟量子比特中

Beyond-Ten-Hour Coherence in a Decoherence-Free Trapped-Ion Clock Qubit

本文通过结合钟态量子比特与去相干自由子空间编码，实现了超过十小时的相干性，突破了传统技术限制，为可扩展的量子信息处理奠定了基础。

利用受限均匀磁场证明宏观量子相干性

Evidencing Macroscopic Quantum Coherence using Confined Uniform Magnetic Field

本文提出一种利用受限均匀磁场创建并认证宏观物体相干叠加的新方案，通过自旋-空间纠缠实现仅用自旋测量认证，并基于NV色心纳米金刚石分析了其可行性。

A long-lived Zeeman trapped-ion qubit

We demonstrate a coherence time of 2.1(1)~s for electron spin superposition states of a single trapped $^{40}$Ca$^+$ ion. The coherence time, measured with a spin-echo experiment, corresponds to residual rms magnetic field fluctuations $\leq$~2.7$\times$10$^{-12}$~T. The suppression of decoherence induced by fluctuating magnetic fields is achieved by combining a two-layer $μ$-metal shield, which reduces external magnetic noise by 20 to 30~dB for frequencies of 50~Hz to 100~kHz, with Sm$_2$Co$_{17}$ permanent magnets for generating a quantizing magnetic field of 0.37~mT. Our results extend the …

分子在高纯度固态反氢中的长核自旋相干时间

Long nuclear spin coherence times for molecules trapped in high-purity solid parahydrogen

研究分子在高纯度固态反氢中测量自旋弛豫时间与相干时间，发现更高纯度矩阵可延长相干时间，揭示反氢矩阵对相干时间的限制。

一种利用偏振基控制产生宏观量子特征的相干方法及其对激光的投影测量

A coherence method generating macroscopic quantum features using polarization-basis control and its projection measurements of laser light

本文提出纯相干方法，通过偏振基控制和线性光学投影测量，使常规激光的正交偏振光对具备不可区分性，从而产生宏观量子特征并揭示 Bell 态所需的固定相位条件。

利用连续波激光的偏振-路径相干操控实现宏观量子关联

Macroscopic quantum correlation using coherence manipulations of polarization-path correlations of a continuous-wave laser

本文提出通过非干涉 Mach-Zehnder 干涉仪中的电光和声光调制器操控连续波激光的偏振-路径相干性，实现不可分离乘积基形式的宏观量子关联。

Autofeedback scheme for preservation of macroscopic coherence in microwave cavities

We present a scheme for controlling the decoherence of a linear superposition of two coherent states with opposite phases in a high-Q microwave cavity, based on the injection of appropriately prepared ``probe'' and ``feedback'' Rydberg atoms, improving the one presented in [D. Vitali et al., Phys. Rev. Lett. 79, 2442 (1997)]. In the present scheme, the information transmission from the probe to the feedback atom is directly mediated by a second auxiliary cavity. The detection efficiency for the probe atom is no longer a critical parameter, and the decoherence time of the superposition state ca…

Coherence properties of highly-excited motional states of a trapped ion

We present a study of the coherence properties of a variety of motional states of a single ion confined in a Penning ion trap. We demonstrate that the motion of the ion has a coherence time of the order of one second, using Ramsey interferometry. We introduce a technique for preparing the ion in an incoherent superposition of highly-excited motional states using a simple modification of optical sideband cooling. Coherent manipulation of these states allow measurements of optical and motional coherence to be carried out. We show that these highly-excited motional state superpositions have long …

关于在受控离子链中径向局部声子跃迁的退相干研究

Study of decoherence in radial local phonon hopping within trapped-ion string

研究了受控离子链径向局部声子跃迁的退相干机制，通过测量跃迁衰减与阱参数的关系，揭示了非线性耦合对退相干的影响，为评估声子跃迁相干性提供了方法。

多模囚禁原子系综中相互作用辅助的自旋相干性

Interaction-Assisted Spin Coherence in a Multimode Trapped Atomic Ensemble

本文研究多模囚禁原子系综中热占据导致的拉姆齐对比度衰减，提出弱轴分辨哈密顿理论，发现交换相互作用可恢复集体相干性，且交叉耦合遵循逆平方热标度。

光移抑制的精密偏振调谐在囚禁离子量子比特中的应用

Precision Polarization Tuning for Light Shift Mitigation in Trapped-Ion Qubits

本研究通过精确调谐偏振，显著抑制囚禁离子量子比特的光移，使时钟量子比特相干时间提升百倍以上，塞曼量子比特提升十倍以上，推进可扩展量子处理器实现。

Criteria for generalized macroscopic and mesoscopic quantum coherence

We consider macroscopic, mesoscopic and "S-scopic" quantum superpositions of eigenstates of an observable, and develop some signatures for their existence. We define the extent, or size $S$ of a superposition, with respect to an observable \hat{x}, as being the range of outcomes of \hat{x} predicted by that superposition. Such superpositions are referred to as generalized $S$-scopic superpositions to distinguish them from the extreme superpositions that superpose only the two states that have a difference $S$ in their prediction for the observable. We also consider generalized $S$-scopic super…

Gate fidelity, dephasing, and "magic" trapping of optically trapped neutral atom

The fidelity of the gate operation and the coherence time of neutral atoms trapped in an optical dipole trap are figures of merit for the applications. The motion of the trapped atom is one of the key factors which influence the gate fidelity and coherence time. The motion has been considered as a classical oscillator in analyzing the influence. Here we treat the motion of the atom as a quantum oscillator. The population on the vibrational states of the atom are considered in analyzing the gate fidelity and decoherence. We show that the fidelity of a coherent rotation gate is dramatically limi…

Experimental demonstrations for randomness-based macroscopic Franson-type nonlocal correlation using coherently coupled photons

Franson-type nonlocal quantum correlation based on the particle nature of quantum mechanics has been intensively studied for both fundamental physics and potential applications of quantum key distribution between remotely separated parties over the last several decades. Recently, a coherence theory of deterministic quantum features has been applied for Franson-type nonlocal correlation [arXiv:2102.06463] to understand its quantumness in a purely classical manner, where the resulting features are deterministic and macroscopic. Here, nearly sub-Poisson distributed coherent photon pairs obtained …

Macroscopic Quantum Coherence in a Magnetic Nanoparticle Above the Surface of a Superconductor

We study macroscopic quantum tunneling of the magnetic moment in a single-domain particle placed above the surface of a superconductor. Such a setup allows one to manipulate the height of the energy barrier, preserving the degeneracy of the ground state. The tunneling amplitude and the effect of the dissipation in the superconductor are computed.

Synthesis and characterization of entangled mesoscopic superpositions for a trapped electron

We propose a scheme for the generation and reconstruction of entangled states between the internal and external (motional) degrees of freedom of a trapped electron. Such states also exhibit quantum coherence at a mesoscopic level.

Macroscopic quantum superposition of spin ensembles with ultra-long coherence times via superradiant masing

Macroscopic quantum phenomena such as lasers, Bose-Einstein condensates, superfluids, and superconductors are of great importance in foundations and applications of quantum mechanics. In particular, quantum superposition of a large number of spins in solids is highly desirable for both quantum information processing and ultrasensitive magnetometry. Spin ensembles in solids, however, have rather short collective coherence time (typically less than microseconds). Here we demonstrate that under realistic conditions it is possible to maintain macroscopic quantum superposition of a large spin ensem…

Spin self-rephasing and very long coherence times in a trapped atomic ensemble

We perform Ramsey spectroscopy on the ground state of ultra-cold 87Rb atoms magnetically trapped on a chip in the Knudsen regime. Field inhomogeneities over the sample should limit the 1/e contrast decay time to about 3 s, while decay times of 58 s are actually observed. We explain this surprising result by a spin self-rephasing mechanism induced by the identical spin rotation effect originating from particle indistinguishability. We propose a theory of this synchronization mechanism and obtain good agreement with the experimental observations. The effect is general and susceptible to appear i…

Coherence properties of nanofiber-trapped cesium atoms

We experimentally study the ground state coherence properties of cesium atoms in a nanofiber-based two-color dipole trap, localized 200 nm away from the fiber surface. Using microwave radiation to coherently drive the clock transition, we record Ramsey fringes as well as spin echo signals and infer a reversible dephasing time $T_2^\ast=0.6$ ms and an irreversible dephasing time $T_2^\prime=3.7$ ms. By theoretically modelling the signals, we find that, for our experimental parameters, $T_2^\ast$ and $T_2^\prime$ are limited by the finite initial temperature of the atomic ensemble and the heatin…

Macroscopic Schrödinger Cat Resistant to Particle Loss and Local Decoherence

The Schrödinger cat state plays a crucial role in quantum theory, and has important fundamental as well as technological implications, ranging from quantum measurement theory to quantum computers. The power of the potential implications of the cat state lies in the quantum coherence, as measured by the degree of entanglement, between its microscopic and macroscopic sectors. We show that in contrast to other cat states, it is possible to choose the states of the macroscopic sector in a way that the resulting cat state, which we term as the W-cat state, has quantum coherence that is resistant to…

Analysis of nonclasscial features in a coupled macroscopic binary system

Nonclassical phenomena of quantum mechanics such as anticorrelation and photonic de Broglie waves (PBWs) have been recently understood as a special case of coherence optics with a particular phase relation between orthogonal bases composing a classical system. Such a macroscopic understanding of nonclassical features has also been confirmed experimentally for a coherence version of PBWs in a doubly-coupled Mach-Zehnder interferometer (MZI). Here, a multi-coupled MZI system is analyzed and discussed to obtain a general understanding of the nonclassical feature using tensor products of binary ba…

Feasibility of a quantum memory for continuous variables based on trapped ions

We propose to use a large cloud of cold trapped ions as a medium for quantum optics and quantum information experiments. Contrary to most recent realizations of qubit manipulation based on a small number of trapped and cooled ions, we study the case of traps containing a macroscopic number of ions. We consider in particular the implementation of a quantum memory for quantum information stored in continuous variables and study the impact of the relevant physical parameters on the expected performances of the system.

Implications of surface noise for the motional coherence of trapped ions

Electric noise from metallic surfaces is a major obstacle towards quantum applications with trapped ions due to motional heating of the ions. Here, we discuss how the same noise source can also lead to pure dephasing of motional quantum states. The mechanism is particularly relevant at small ion-surface distances, thus imposing a new constraint on trap miniaturization. By means of a free induction decay experiment, we measure the dephasing time of the motion of a single ion trapped 50~$μ$m above a Cu-Al surface. From the dephasing times we extract the integrated noise below the secular frequen…

基于宏观相干的光学量子存储

Optical quantum memory on macroscopic coherence

本文提出利用预先建立的宏观量子相干实现光学量子存储，在非均匀展宽原子系综中实现低噪声、可编程和按需读取，为稀土掺杂晶体和拉曼原子气体中的量子存储发展开辟新途径。

Noise induced interference fringes in trapped ultracold bosonic gases

We study the dynamics of ultracold atoms trapped in optical double-well potentials in presence of noise generated by an external environment. When prepared in a Fock number state, the system shows phase coherence in the averaged density profile obtained using standard absorption image techniques, that disappears in absence of noise. This effect indicates that also in many-body systems an external environment may enhance quantum coherence, instead of destroying it.

通过光学四次势阱增强中性原子的相干时间

Enhancing the coherence time of a neutral atom by an optical quartic trap

本文提出利用高阶空间形式的光学偶极阱（如四次势阱）来降低退相干率，并通过实验验证了该方法能有效增强囚禁中性原子的相干时间。

A fast scheme for the implementation of the quantum Rabi model with trapped ions

We show how to produce a fast quantum Rabi model with trapped ions. Its importance resides not only in the acceleration of the phenomena that may be achieved with these systems, from quantum gates to the generation of nonclassical states of the vibrational motion of the ion, but also in reducing unwanted effects such as the decay of coherences that may appear in such systems.

环境条件下超辐射固体中的持续宏观量子相干性

Sustained macroscopic quantum coherence in a superradiant solid under ambient conditions

本研究在环境条件下实现固态超辐射脉泽，在金刚石氮-空位中心自旋与微波腔光子间建立长寿命宏观量子相干性，为多体关联量子光探索提供固态平台。

Preservation of atomic coherence in double-well optical lattice in presence of decoherence

We present a quantum interference approach to preserve coherence in the external states of an atom trapped in an optical lattice. We show that this is possible by suitably choosing the initial state of the atom. We demonstrate this in context of decoherence due to spontaneous emission in an one-dimensional optical double-well lattice.

An investigation into why macroscopic systems behave classically

We study why it is quite so hard to make a superposition of superfluid flows in a Bose-Einstein condensate. To do this we initially investigate the quantum states of $N$ atoms trapped in a 1D ring with a barrier at one position and a phase applied around it. We show how macroscopic superpositions can in principle be produced and investigate factors which affect the superposition. We then use the Bose-Hubbard model to study an array of Bose-Einstein condensates trapped in optical potentials and coupled to one another to form a ring. We derive analytic expressions for the quality of the superpos…

Macroscopic coherence between quantum condensates formed at different times

We demonstrate macroscopic coherence between quantum condensates generated at different times, separated by more than the particle dephasing time. This is possible due to the dressed light-matter nature of exciton-polaritons, which can be injected resonantly by optical excitation at well-defined momenta. We show that the build-up of coherence between condensates depends on the interaction between the particles, particle density, as well as temperature despite the non-equilibrium nature of the condensate, whereas the mass of the particles plays no role in the condensation of resonantly injected…

Long-lived Quantum Coherence between Macroscopically Distinct States in Superradiance

The dephasing influence of a dissipative environment reduces linear superpositions of macroscopically distinct quantum states (sometimes also called Schrödinger cat states) usually almost immediately to a statistical mixture. This process is called decoherence. Couplings to the environment with a certain symmetry can lead to slow decoherence. In this Letter we show that the collective coupling of a large number of two-level atoms to an electromagnetic field mode in a cavity that leads to the phenomena of superradiance has such a symmetry, at least approximately. We construct superpositions of …

Extended coherence time on the clock transition of optically trapped Rubidium

Optically trapped ensembles are of crucial importance for frequency measurements and quantum memories, but generally suffer from strong dephasing due to inhomogeneous density and light shifts. We demonstrate a drastic increase of the coherence time to 21 s on the magnetic field insensitive clock transition of Rb-87 by applying the recently discovered spin self-rephasing. This result confirms the general nature of this new mechanism and thus shows its applicability in atom clocks and quantum memories. A systematic investigation of all relevant frequency shifts and noise contributions yields a s…

Quantum interference from remotely trapped ions

We observe quantum interference of photons emitted by two continuously laser-excited single ions, independently trapped in distinct vacuum vessels. High contrast two-photon interference is observed in two experiments with different ion species, calcium and barium. Our experimental findings are quantitatively reproduced by Bloch equation calculations. In particular, we show that the coherence of the individual resonance fluorescence light field is determined from the observed interference.

A macroscopic quantum state analysed particle by particle

Explaining how microscopic entities collectively produce macroscopic phenomena is a fundamental goal of many-body physics. Theory predicts that large-scale entanglement is responsible for exotic macroscopic phenomena, but observation of entangled particles in naturally occurring systems is extremely challenging. Synthetic quantum systems made of atoms in optical lattices have been con- structed with the goal of observing macroscopic quantum phenomena with single-atom resolution. Serious challenges remain in producing and detecting long-range quantum correlations in these systems, however. Here…

Suppression of Dephasing of Optically Trapped Atoms

Ultra-cold atoms trapped in an optical dipole trap and prepared in a coherent superposition of their hyperfine ground states, decohere as they interact with their environment. We demonstrate than the loss in coherence in an "echo" experiment, which is caused by mechanisms such as Rayleigh scattering, can be suppressed by the use of a new pulse sequence. We also show that the coherence time is then limited by mixing to other vibrational levels in the trap and by the finite lifetime of the internal quantum states of the atoms.

Study of Macroscopic Coherence and Decoherence in the SQUID by Adiabatic Inversion

We suggest a procedure for demonstrating quantum coherence and measuring decoherence times between different fluxoid states of a SQUID by using ``adiabatic inversion'', where one macroscopic fluxoid state is smoothly transferred into the other, like a spin reversing direction by following a slowly moving magnetic field. This is accomplished by sweeping an external applied flux, and depends on a well-defined quantum phase between the two macroscopic states. Varying the speed of the sweep relative to the decoherence time permits one to move from the quantum regime, where such a well-defined phas…

量子等化与简正态热化假说作为观察宏观量子叠加的限制

Equilibration and the eigenstate thermalization hypothesis as limits to observing macroscopic quantum superpositions

研究揭示了在完美隔离下，单元arity动力学通过简正态热化假说和随机矩阵理论抑制宏观相干特征，展示GHZ态在多数时间内无法区分叠加与经典混合，等化过程限制了宏观量子效应的观测。

A long-lived memory qubit on a low-decoherence quantum bus

We demonstrate long-lived coherence in internal hyperfine states of a single \Ca{43} trapped-ion qubit $[T_2=1.2(2)\s]$, and in external motional states of a single \Ca{40} trapped-ion qubit $[T_2'=0.18(4)\s]$, in the same apparatus. The motional decoherence rate is consistent with the heating rate, which was measured to be 3(1) quanta/sec. Long coherence times in the external motional states are essential for performing high-fidelity quantum logic gates between trapped-ion qubits. The internal-state $T_2$ time that we observe in \Ca{43}, which has not previously been used as a trapped-ion qub…

Second-Scale Nuclear Spin Coherence Time of Trapped Ultracold $^{23}$Na$^{40}$K Molecules

Coherence, the stability of the relative phase between quantum states, lies at the heart of quantum mechanics. Applications such as precision measurement, interferometry, and quantum computation are enabled by physical systems that have quantum states with robust coherence. With the creation of molecular ensembles at sub-$μ$K temperatures, diatomic molecules have become a novel system under full quantum control. Here, we report on the observation of stable coherence between a pair of nuclear spin states of ultracold fermionic NaK molecules in the singlet rovibrational ground state. Employing m…

Study of decoherence of a superposition of macroscopic quantum states by means the consideration of a multimode state of a Schrodinger cat

Quantum Schrodinger cat states are of great interest in quantum communications and quantum optics. These states are used in various scientific fields such as quantum computing, quantum error correction and high-precision measurements. The analysis of the Schrodinger cat states coherence is an important task for their complete practical application. Our developed approach makes it possible to estimate the coherence of the quantum Schrodinger cat state of arbitrary dimension, as well as to find the interference visibility of the state - an important optical characteristic. The obtained simple qu…

Manipulation and Detection of a Trapped Yb+ Ion Hyperfine Qubit

We demonstrate the use of trapped ytterbium ions as quantum bits for quantum information processing. We implement fast, efficient state preparation and state detection of the first-order magnetic field-insensitive hyperfine levels of 171Yb+, with a measured coherence time of 2.5 seconds. The high efficiency and high fidelity of these operations is accomplished through the stabilization and frequency modulation of relevant laser sources.

Signatures of macroscopic quantum coherence in ultracold dilute Fermi gases

We propose a double-well configuration for optical trapping of ultracold two-species Fermi-Bose atomic mixtures. Two signatures of macroscopic quantum coherence attributable to a superfluid phase transition for the Fermi gas are analyzed. The first signature is based upon tunneling of Fermi pairs when the power of the deconfining laser beam is significantly reduced. The second relies on the observation of interference fringes in a regime where the fermions are trapped in two sharply separated minima of the potential. Both signatures rely on small decoherence times for the Fermi samples, which …