We introduce a matter wave interference scheme based on the quantization of orbital angular momentum in a ring trap. It operates without beam splitters, is sensitive to geometric phases induced by external gauge fields, and allows measuring interatomic scattering lengths. We argue that orbital angular momentum interferometry offers a versatile platform for quantum coherent experiments with cold atoms and Bose-Einstein condensates using state-of-the-art technology.
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.
We collect the fluorescence from two trapped atomic ions, and measure quantum interference between photons emitted from the ions. The interference of two photons is a crucial component of schemes to entangle atomic qubits based on a photonic coupling. The ability to preserve the generated entanglement and to repeat the experiment with the same ions is necessary to implement entangling quantum gates between atomic qubits, and allows the implementation of protocols to efficiently scale to larger numbers of atomic qubits.
Taking recent experiments as examples, we discuss the conditions for sub-wavelength probing of optical field structures by single trapped atoms. We calculate the achievable resolution, highlighting its connection to the fringe visibility in an interference experiment. We show that seemingly different physical pictures, such as spatial averaging, phase modulation, and which-way information, describe the situation equally and lead to identical results. The connection to Bohr's moving slit experiment is pointed out.
Quantum repeater segment with free-space coupled co-trapped ions using telecom photon interference
Universität des Saarlandes（萨尔兰大学）；Zentrum für Quantentechnologien (QuTe), Universität des Saarlandes（萨尔兰大学量子技术中心 (QuTe)）；Ruhr-Universität Bochum（波鸿鲁尔大学）
When two indistinguishable single photons are fed into the two input ports of a beam splitter, the photons will coalesce and leave together from the same output port. This is a quantum interference effect, which occurs because the two possible paths where the photons leave in different output ports interfere destructively. This effect was first observed in parametric downconversion by Hong, Ou and Mandel, and then with single photons produced one after the other by the same quantum emitter. With the recent development of quantum information, a lot of attention has been devoted to this coalesce…
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.
The scheme recently proposed in [M. Scala et al., Phys Rev Lett 111, 180403 (2013)], where a gravity-dependent phase shift is induced on the spin of a nitrogen-vacancy (NV) center in a trapped nanodiamond by the interaction between its magnetic moment and the quantized motion of the particle, provides a way to detect spatial quantum superpositions by means of spin measurements only. Here, the effect of unwanted coupling with other motional degrees of freedom is considered and we show that it does not affect the validity of the scheme. Both this coupling and the additional error source due to m…
The demonstration of optical multipath interference from a large number of quantum emitters is essential for the realization of many paradigmatic experiments in quantum optics. However, such interference remains still unexplored as it crucially depends on the sub-wavelength positioning accuracy and stability of all emitters. We present the observation of controlled interference of light scattered from strings of up to 53~trapped ions. The light scattered from ions localized in a harmonic trapping potential is collected along the ion crystal symmetry axis, which guarantees the spatial indisting…
The quantum walk (QW), as the quantum analog of classical random walk, provides a feasible platform to study the topological phenomenon and non-equilibrium dynamics. Here, we propose a novel scheme to realize the quantum walk with a single trapped ion where the Fock states provides the walk space and zero phonon state $\left|n=0\right\rangle $ serves as its natural boundary. Thus, our scheme offers the unique opportunity to investigate the dynamics of the bound states of the corresponding topological systems. Particularly, the quench dynamics of the bound states can be extensively studied by t…
We present an optical scheme to detect the oscillations of a two-ion string confined in a linear Paul trap. The motion is detected by analyzing the intensity correlations in the fluorescence light emitted by one or two ions in the string. We present measurements performed under continuous Doppler cooling and under pulsed illumination. We foresee several direct applications of this detection method, including motional analysis of multi-ion species or coupled mechanical oscillators, and sensing of mechanical correlations.
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 …
We apply wave packet methods to study an ion-trap system in the strong excitation regime imposing neither the rotating wave nor the Lamb-Dicke approximations. By this approach we show the existence of states with restricted phase space evolution, as a genuine consequence of quantum interference between wave packet fractions. A particular instance of such a state oscillates between maximal entanglement and pure disentanglement between the constitute subsystems. The characteristic crossover time is very rapid making them suitable for state preparations of EPR or Schrodinger cat states. Over long…
The subject of bianyon interference with ultracold atoms is introduced through theoretical investigations pertaining to the second-order momentum correlation maps of two anyons (built upon spinless and spin-1/2 bosonic, as well as spin-1/2 fermionic ultracold atoms) trapped in a double-well optical trap. The two-particle system is modeled according to the recently proposed protocols for emulating an anyonic Hubbard Hamiltonian in ultracold-atom one-dimensional lattices. Because the second-order momentum correlations are mirrored in the time-of-flight second-order interference patterns in space…
We report on a demonstration of Ramsey interferometry by three-dimensional motion with a trapped $^{171}Yb^+$ ion. We applied a momentum kick to the ion in a direction diagonal to the trap axes to initiate three-dimensional motion using a mode-locked pulse laser. The interference signal was analyzed theoretically to demonstrate three-dimensional matter-wave interference. This work paves the way to realizing matter-wave interferometry using trapped ions.
Trapped atomic ions embedded in optical cavities are a promising platform to enable long-distance quantum networks and their most far-reaching applications. Here we achieve and analyze photon indistinguishability in a telecom-converted ion-cavity system. First, two-photon interference of cavity photons at their ion-resonant wavelength is observed and found to reach the limits set by spontaneous emission. Second, this limit is shown to be preserved after a two-step frequency conversion replicating a distributed scenario, in which the cavity photons are converted to the telecom C band and then b…
The superpositional wave function oscillations for finite-time implementation of quantum algorithms modifies the desired interference required for quantum computing. We propose a scheme with trapped ultracold ion-pairs being qubits to diminish the detrimental effect of the wave function oscillations, and apply the scheme to the two-qubit Grover's search. It can be also found that the qubits in our scheme are more robust against the decoherence caused by the environment, and the model is scalable.
We propose a scheme to perform probabilistic quantum gates on remote trapped atom qubits through interference of optical frequency qubits. The method does not require localization of the atoms to the Lamb-Dicke limit, and is not sensitive to interferometer phase instabilities. Such probabilistic gates can be used for scalable quantum computation.
We present a robust and fast laser cooling scheme suitable for trapped atoms and ions. Based on quantum interference, generated by a special laser configuration, it is able to rapidly cool the system such that the final phonon occupation vanishes to zeroth order in the Lamb-Dicke parameter in contrast to existing cooling schemes. Furthermore, it is robust under conditions of fluctuating laser intensity and frequency, thus making it a viable candidate for experimental applications.
The uncertainty relation between angle and orbital angular momentum had not been formulated in a similar form as the uncertainty relation between position and linear momentum because the angle variable is not represented by a quantum mechanical self-adjoint operator. Instead of the angle variable operator, we introduce the complex position operator $ \hat{Z} = \hat{x}+i \hat{y} $ and interpret the order parameter $ μ= \langle \hat{Z} \rangle / \sqrt{ \langle \hat{Z}^\dagger \hat{Z} \rangle} $ as a measure of certainty of the angle distribution. We prove the relation between the uncertainty of …
Identification and understanding of the evolution of interference patterns in two-particle momentum correlations as a function of the strength of interatomic interactions are important in explorations of the nature of quantum states of trapped particles. Together with the analysis of two-particle spatial correlations, they offer the prospect of uncovering fundamental symmetries and structure of correlated many-body states, as well as opening vistas into potential control and utilization of correlated quantum states as quantum information resources. With the use of the second-order density matr…
We propose a scheme for conditional implementation of a quantum phase gate by using distant atoms trapped in different optical cavities. Instead of direct interaction between atoms, the present scheme makes use of quantum interference of polarized photons decaying from the optical cavities to conditionally create the desired quantum phase gate between two distant atoms. The proposed scheme only needs linear optical elements and a two-fold coincidence detection, and are insensitive to the quantum noise. The scheme can be directly used to prepare any quantum state of many distant atoms.
The desired interference required for quantum computing may be modified by the wave function oscillations for the implementation of quantum algorithms[Phys.Rev.Lett.84(2000)1615]. To diminish such detrimental effect, we propose a scheme with trapped ion-pairs being qubits and apply the scheme to the Grover search. It can be found that our scheme can not only carry out a full Grover search, but also meet the requirement for the scalable hot-ion quantum computing. Moreover, the ion-pair qubits in our scheme are more robust against the decoherence and the dissipation caused by the environment tha…
We propose to couple an on-chip high finesse superconducting cavity to the lateral-motion and spin state of a single electron trapped on the surface of superfluid helium. We estimate the motional coherence times to exceed 15 microseconds, while energy will be coherently exchanged with the cavity photons in less than 10 nanoseconds for charge states and faster than 1 microsecond for spin states, making the system attractive for quantum information processing and cavity quantum electrodynamics experiments. Strong interaction with cavity photons will provide the means for both nondestructive read…
We study an ultra-cold gas of $N$ bosons trapped in a one dimensional $M$-site optical lattice perturbed by a spatially dependent potential $g\cdot x^j$, where the unknown coupling strength $g$ is to be estimated. We find that the measurement uncertainty is bounded by $Δg\propto\frac1{N (M^j-1)}$. For a typical case of a linear potential, the sensitivity improves as $M^{-1}$, which is a result of multiple interferences between the sites -- an advantage of multi-path interferometers over the two-mode setups. Next, we calculate the estimation sensitivity for a specific measurement where, after t…
Trapped ion crystals have proved to be one of the most viable physical implementations of quantum registers and a promising candidate for a scalable realization of quantum networks. The latter will require the development of an efficient interface between trapped ions and photons. We describe two research directions that are currently investigated to realize such photonic quantum interfaces in free space using high numerical aperture optics. The first approach investigates how strong focusing of light onto a single ion can increase the interaction strength to achieve efficient interaction betw…
We investigate the feasibility of observing matter-wave interference of a micron-sized charged particle by putting it into a quantum superposition of states with a distinguishable separation. In the proposed method, an atomic ion is confined in a linear Paul trap along with the massive charged particle so that we can make use of the extensive toolbox of experimental techniques developed to control quantum states of trapped ions, and to manipulate their motions with high fidelity operations. This approach provides a stringent test of the predictions of dynamical reduction models of delocalised …
We study the interaction of a light beams carrying angular momentum with a single, trapped and well localized ion. We provide a detailed calculation of selection rules and excitation probabilities for quadrupole transitions. The results show the dependencies on the angular momentum and polarization of the laser beam as well as the direction of the quantization magnetic field. In order to observe optimally the specific effects, focusing the angular momentum beam close to the diffraction limit is required. We discuss a protocol for examining experimentally the effects on the S$_{1/2}$ to D$_{5/2…
Elucidating similarities and differences between quantum-optics biphoton interference phenomena and the quantum physics of quasi-one-dimensional double-well optically-trapped ultracold neutral bosonic or fermionic atoms, we show that the analog of the optical biphoton joint-coincidence spectral correlations, studied with massless non-interacting biphotons emanating from EPR-Bell-Bohm single-occupancy sources, corresponds to a distinct contribution in the total second-order momentum correlations of the massive, interacting, and time-evolving ultracold atoms. This single-occupancy contribution c…
We propose a quantum interference cooling scheme for a nano-mechanical resonator (NAMR) in a hybrid optomechanical system, where the atoms are trapped in an optomechanical cavity, coupling to an additional optical cavity. The absorption of the optomechanical resonator can be modified by quantum interference effects induced by the atom-cavity and cavity-cavity couplings independently. With the employment of the quantum interference, the desired transition for cooling is enhanced, along with the heating suppression due to the undesired transition. As a result, the NAMR vibration can be cooled do…
Atoms trapped in a red detuned retro-reflected Laguerre-Gaussian beam undergo orbital motion within rings whose centers are on the axis of the laser beam. We determine the wave functions, energies and degeneracies of such quantum rotors (QRs), and the microwave transitions between the energy levels are elucidated. We then show how such QR atoms can be used as high-accuracy rotation sensors when the rings are singly-occupied.
We address the influence of the molecular orbital geometry and of the molecular alignment with respect to the laser-field polarization on laser-induced nonsequential double ionization of diatomic molecules for different molecular species, namely $\mathrm{N}_2$ and $\mathrm{Li}_2$. We focus on the recollision excitation with subsequent tunneling ionization (RESI) mechanism, in which the first electron, upon return, promotes the second electron to an excited state, from where it subsequently tunnels. We show that the electron-momentum distributions exhibit interference maxima and minima due to t…
Quantum carpets- in position and momentum space- woven by the self-interference of de Broglie wave of an atom or an electron, trapped in an infinitely deep potential well, are explained. The recurrence of self-similar structures in designs of these carpets mimics the phenomena of quantum revivals and fractional revivals. We identify fractional revivals of various order by means of these space-time and momentum-time interference patterns.
We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.
Orbital Hall Effect in Weyl Semimetals from quantum geometric band interference
University of Bologna（博洛尼亚大学）；Max Planck Institute for the Structure and Dynamics of Matter（马普结构动力学研究所）；Universität Würzburg（维尔茨堡大学）；Universidad del País Vasco（巴斯克大学）；The Flatiron Institute（平顿研究所）
A semiconductor nanowire based superconductor-normal-superconductor (SNS) junction is modeled theoretically. A magnetic field is applied along the nanowire axis, parallel to the current. The Bogoliubov-de Gennes equations for Andreev bound states are solved while considering the electronic subbands due to radial confinement in the N-section. The energy-versus-phase curves of the Andreev bound states shift in phase as the N-section quasiparticles with orbital angular momentum couple to the axial field. A similar phase shift is observed in the continuum current of the junction. The quantum mecha…
Quantum interferometers are generally set so that phase differences between paths in coordinate space combine constructive or destructively. Indeed, the interfering paths can also meet in momentum space leading to momentum-space fringes. We propose and analyze a method to produce interference in momentum space by phase-imprinting part of a trapped atomic cloud with a detuned laser. For one-particle wave functions analytical expressions are found for the fringe width and shift versus the phase imprinted. The effects of unsharpness or displacement of the phase jump are also studied, as well as m…
We present protocols for dissipative entanglement of three trapped-ion qubits and discuss a scheme that uses sympathetic cooling as the dissipation mechanism. This scheme relies on tailored destructive interference to generate any one of six entangled W states in a three-ion qubit space. Using a beryllium-magnesium ion crystal as an example system, we theoretically investigate the protocol's performance and the effects of likely error sources, including thermal secular motion of the ion crystal, calibration imperfections, and spontaneous photon scattering. We estimate that a fidelity of $\sim$…
We theoretically investigate transport signatures of quantum interference in highly symmetric double quantum dots in a parallel geometry and demonstrate that extremely weak symmetry-breaking effects can have a dramatic influence on the current. Our calculations are based on a master equation where quantum interference enters as non-diagonal elements of the density matrix of the double quantum dots. We also show that many results have a physically intuitive meaning when recasting our equations as Bloch-like equations for a pseudo spin associated with the dot occupation. In the perfectly symmetr…
For an atomic condensate in an axially symmetric magnetic trap, the sum of the axial components of the orbital angular momentum and the hyperfine spin is conserved. Inside an Ioffe-Pritchard trap (IPT) whose magnetic field (B-field) is not axially symmetric, the difference of the two becomes surprisingly conserved. In this paper we investigate the relationship between the values of the sum/difference angular momentums for an atomic condensate inside a magnetic trap and the associated gauge potential induced by the adiabatic approximation. Our result provides significant new insight into the vo…
The University of Tokyo（东京大学）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；Institut Néel（奈尔研究所）
In recent cross-disciplinary studies involving both optics and computing, single-photon-based decision-making has been demonstrated by utilizing the wave-particle duality of light to solve multi-armed bandit problems. Furthermore, entangled-photon-based decision-making has managed to solve a competitive multi-armed bandit problem in such a way that conflicts of decisions among players are avoided while ensuring equality. However, as these studies are based on the polarization of light, the number of available choices is limited to two, corresponding to two orthogonal polarization states. Here …
We demonstrate the excitation, using a structured light beam carrying orbital angular momentum, of the center of mass motion of a single atom in the transverse direction to the beam's propagation. This interaction is achieved with a vortex beam carrying one unit of orbital angular momentum and one unit of spin/polarization angular momentum. Using a singly charged $^{40}$Ca$^+$ ion, cooled near the ground state of motion in the 3D harmonic potential of a Paul trap, we probe the narrow S$_{1/2}$ to D$_{5/2}$ transition near $729\,\mathrm{nm}$ on its motional sidebands to quantify the momentum tr…
Analytic higher-order momentum correlation functions associated with the time-of-flight spectroscopy of three ultracold fermionic atoms singly-confined in a linear three-well optical trap are presented, corresponding to the W- and Greenberger-Horne-Zeilinger-type (GHZ) states that belong to characteristic classes of tripartite entanglement and represent the strong-interaction regime captured by a three-site Heisenberg Hamiltonian. The methodology introduced here contrasts with and goes beyond that based on the standard Wick's factorization scheme; it enables determination of both third-order a…
