We develop a theory of quantum feedback cooling of a single ion trapped in front of a mirror. By monitoring the motional sidebands of the light emitted into the mirror mode we infer the position of the ion, and act back with an appropriate force to cool the ion. We derive a feedback master equation along the lines of the quantum feedback theory developed by Wiseman and Milburn, which provides us with cooling times and final temperatures as a function of feedback gain and various system parameters.
The radiation pressure of two detuned laser beams can create a stable trap for a suspended cavity mirror; here it is shown that such a configuration entangles the output light fields via interaction with the mirror. Intra-cavity, the opto-mechanical system can become entangled also. The degree of entanglement is quantified spectrally using the logarithmic negativity. Entanglement survives in the experimentally accessible regime of gram-scale masses subject to thermal noise at room temperature.
Efficient collection and analysis of trapped ion qubit fluorescence is essential for robust qubit state detection in trapped ion quantum computing schemes. We discuss simple techniques of improving photon collection efficiency using high numerical aperture (N.A.) reflective optics. To test these techniques we placed a spherical mirror with an effective N.A. of about 0.9 inside a vacuum chamber in the vicinity of a linear Paul trap. We demonstrate stable and reliable trapping of single barium ions, in excellent agreement with our simulations of the electric field in this setup. While a large N.…
Efficient collection of fluorescence from trapped ions is crucial for quantum optics and quantum computing applications, specifically, for qubit state detection and in generating single photons for ion-photon and remote ion entanglement. In a typical setup, only a few per cent of ion fluorescence is intercepted by the aperture of the imaging optics. We employ a simple metallic spherical mirror integrated with a linear Paul ion trap to achieve photon collection efficiency of at least 10% from a single Ba$^+$ ion. An aspheric corrector is used to reduce the aberrations caused by the mirror and a…
A distant mirror leads to a vacuum-induced level shift in a laser-excited atom. This effect has been measured with a single mirror 25 cm away from a single, trapped barium ion. This dispersive action is the counterpart to the mirror's dissipative effect, which has been shown earlier to effect a change in the ion's spontaneous decay [J. Eschner et al., Nature 413, 495-498 (2001)]. The experimental data are well described by 8-level optical Bloch equations which are amended to take into account the presence of the mirror according to the model in [U. Dorner and P. Zoller, Phys. Rev. A 66, 023816…
We investigate the Wigner-Weisskopf decay of a two level atom in front of an oscillating mirror. This work builds on and extends previous theoretical and experimental studies of the effects of a static mirror on spontaneous decay and resonance fluorescence. The spontaneously emitted field is inherently non-stationary due to the time-dependent boundary conditions and in order to study its spectral distribution we employ the operational definition of the spectrum of non-stationary light due to the seminal work by Eberly and Wodkiewicz. We find a rich dependence of this spectrum as well as of the…
Motivated by a recent experiment [J. Eschner {\it et al.}, Nature {\bf 413}, 495 (2001)], we now present a theoretical study on the fluorescence of an atom in front of a mirror. On the assumption that the presence of the distant mirror and a lens imposes boundary conditions on the electric field in a plane close to the atom, we derive the intensities of the emitted light as a function of an effective atom-mirror distance. The results obtained are in good agreement with the experimental findings.
We investigate the emission of single photons from CdSe/CdS dot-in-rods which are optically trapped in the focus of a deep parabolic mirror. Thanks to this mirror, we are able to image almost the full 4$π$ emission pattern of nanometer-sized elementary dipoles and verify the alignment of the rods within the optical trap. From the motional dynamics of the emitters in the trap we infer that the single-photon emission occurs from clusters comprising several emitters. We demonstrate the optical trapping of rod-shaped quantum emitters in a configuration suitable for efficiently coupling an ensemble…
Quantum fluctuations of the vacuum are both a surprising and fundamental phenomenon of nature. Understood as virtual photons flitting in and out of existence, they still have a very real impact, \emph{e.g.}, in the Casimir effects and the lifetimes of atoms. Engineering vacuum fluctuations is therefore becoming increasingly important to emerging technologies. Here, we shape vacuum fluctuations using a "mirror", creating regions in space where they are suppressed. As we then effectively move an artificial atom in and out of these regions, measuring the atomic lifetime tells us the strength of t…
The efficient interaction between single photons and single matter objects in free space is of key importance for quantum technologies. An experimental setup for testing this possibility involves single two-level ion trapped at the focus of a parabolic metallic mirror. We study the conditions for the setup, under which the assumption about the free-space mode structure of the radiation field in the vicinity of the atom is justified. In our analysis we apply vectorial properties of light by including polarization degree of freedom. We look for possible changes in the spontaneous emission rate o…
We consider a quantum emitter ("atom") radiating in a one-dimensional (1D) photonic waveguide in the presence of a single mirror, resulting in a delay differential equation for the atomic amplitude. We carry out a systematic analysis of the non-Markovian (NM) character of the atomic dynamics in terms of refined, recently developed notions of quantum non-Markovianity such as indivisibility and information back-flow. NM effects are quantified as a function of the round-trip time and phase shift associated with the atom-mirror optical path. We find, in particular, that unless an atom-photon bound…
We present a scheme for cavity-assisted generation of hybrid entanglement between a moving mirror belonging to an optomechanical cavity and a single trapped ion located inside a second cavity. Due to radiation pressure, it is possible to entangle the moving mirror with one of the cavity fields. Also, by tuning the second cavity field with the internal degrees of freedom of the ion, an entangled state of the cavity field/ion can be independently generated. The fields leaking from each cavity are then combined in a beam-splitter, and following the detection of the outgoing photons by convenientl…
We investigate three types of amplification processes for light fields coupling to an atom near the end of a one-dimensional semi-infinite waveguide. We consider two setups where a drive creates population inversion in the bare or dressed basis of a three-level atom and one setup where the amplification is due to higher-order processes in a driven two-level atom. In all cases, the end of the waveguide acts as a mirror for the light. We find that this enhances the amplification in two ways compared to the same setups in an open waveguide. Firstly, the mirror forces all output from the atom to t…
We investigate the Landau-Zener-Stuckelberg-Majorana interferometry of a superconducting qubit in a semi-infinite transmission line terminated by a mirror. The transmon-type qubit is at the node of the resonant electromagnetic (EM) field, hiding from the EM field. "Mirror, mirror" briefly describes this system, because the qubit acts as another mirror. We modulate the resonant frequency of the qubit by applying a sinusoidal flux pump. We probe the spectroscopy by measuring the reflection coefficient of a weak probe in the system. Remarkable interference patterns emerge in the spectrum, which c…
Various lower- and higher-order nonclassical properties have been studied for two physical systems- (i) an optomechanical system composed of a Fabry-Perot cavity with one nonlinearly oscillating mirror and (ii) an optomechanical-like system formed using a Bose-Einstein condensate (BEC) trapped inside an optical cavity. The investigation is performed using a perturbation method that leads to closed form analytic expressions for the time evolution of the relevant bosonic operators. In the first system, it is observed that the radiation pressure coupling leads to the emergence of lower- and highe…
We theoretically investigate resonant dipole-dipole interaction (RDDI) between artificial atoms in a 1D geometry, implemented by N transmon qubits coupled through a transmission line. Similarly to the atomic cases, RDDI comes from exchange of virtual photons of the unexcited modes, and causes the so-called collective Lamb shift (CLS). To probe the shift, we effectively set one end of the transmission line as a mirror, and examine the reflection spectrum of the probe field from the other end. Our calculation shows that when a qubit is placed at the node of the standing wave formed by the incide…
In this paper we describe a scheme for state transfer between a trapped atomic Bose condensate and an optomechanical end-mirror mediated by a cavity field. Coupling between the mirror and the cold gas arises from the fact that the cavity field can produce density oscillations in the gas which in turn acts as an internal Bragg mirror for the field. After adiabatic elimination of the cavity field we find that the hybrid system of the gas and mirror is described by a beam splitter Hamiltonian that allows for state transfer, but only if the quantum nature of the cavity field is retained.
By tightly focussing a laser field onto a single cold ion trapped in front of a far-distant dielectric mirror, we could observe a quantum electrodynamic effect whereby the ion behaves as the optical mirror of a Fabry-Pérot cavity. We show that the amplitude of the laser field is significantly altered due to a modification of the electromagnetic mode structure around the atom in a novel regime in which the laser intensity is already changed by the atom alone. e propose a direct application of this system as a quantum memory for single photons.
Each natural mode of the electromagnetic field within a parabolic mirror exhibits spatial localization and polarization properties that can be exploited for the quantum control of its interaction with atomic systems. The region of localization is not restricted to the focus of the mirror leading to a selective response of atomic systems trapped on its vicinity. We report calculations of the spontaneous emission rates for an atom trapped inside the mirror accounting for all atomic polarizations and diverse trapping regions. It is shown that electric dipole transitions can be enhanced near the f…
We consider an atom (represented by a two-level system) moving in front of a dielectric plate, and study how traces of dissipation and decoherence (both effects induced by vacuum field fluctuations) can be found in the corrections to the unitary geometric phase accumulated by the atom. We consider the particle to follow a classical, macroscopically-fixed trajectory and integrate over the vacuum field and the microscopic degrees of freedom of both the plate and the particle in order to calculate friction effects. We compute analytically and numerically the non-unitary geometric phase for the mo…
An excited-state atom whose emitted light is back-reflected by a distant mirror can experience trapping forces, because the presence of the mirror modifies both the electromagnetic vacuum field and the atom's own radiation reaction field. We demonstrate this mechanical action using a single trapped barium ion. We observe the trapping conditions to be notably altered when the distant mirror is shifted by an optical wavelength. The well-localised barium ion enables the spatial dependence of the forces to be measured explicitly. The experiment has implications for quantum information processing a…
Photon correlations are investigated for a single laser-excited ion trapped in front of a mirror. Varying the relative distance between the ion and the mirror, photon correlation statistics can be tuned smoothly from an antibunching minimum to a bunching-like maximum. Our analysis concerns the non-Markovian regime of the ion-mirror interaction and reveals the field establishment in a half-cavity interferometer.
Trapped, laser-cooled ions produce intense fluorescence. Detecting this fluorescence enables efficient measurement of quantum state of qubits based on trapped atoms. It is desirable to collect a large fraction of the photons to make the detection faster and more reliable. Additionally, efficient fluorescence collection can improve speed and fidelity of remote ion entanglement and quantum gates. Here we show a novel ion trap design that incorporates metallic spherical mirror as the integral part of the trap itself, being its RF electrode. The mirror geometry enables up to 35% solid angle collec…
The dominant hurdle to the operation of optomechanical systems in the quantum regime is the coupling of the vibrating element to a thermal reservoir via mechanical supports. Here we propose a scheme that uses an optical spring to replace the mechanical support. We show that the resolved-sideband regime of cooling can be reached in a configuration using a high-reflectivity disk mirror held by an optical tweezer as one of the end-mirrors of a Fabry-Perot cavity. We find a final phonon occupation number of the trapped mirror ${\bar n}$= 0.14 for reasonable parameters, well within the quantum regi…
We consider the radiative trapping and cooling of a partially transmitting mirror suspended inside an optical cavity, generalizing the case of a perfectly reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys. Rev. Lett. \textbf{99}, 073601 (2007)]. This configuration was recently used in an experiment to cool a nanometers-thick membrane [Thompson \textit{et al.}, arXiv:0707.1724v2, 2007]. The self-consistent cavity field modes of this system depend strongly on the position of the middle mirror, leading to important qualitative differences in the radiation pressure effe…
We present and characterize fiber mirrors and a miniaturized ion-trap design developed to integrate a fiber-based Fabry-Perot cavity (FFPC) with a linear Paul trap for use in cavity-QED experiments with trapped ions. Our fiber-mirror fabrication process not only enables the construction of FFPCs with small mode volumes, but also allows us to minimize the influence of the dielectric fiber mirrors on the trapped-ion pseudopotential. We discuss the effect of clipping losses for long FFPCs and the effect of angular and lateral displacements on the coupling efficiencies between cavity and fiber. Op…
We demonstrate an all-fiber cavity QED system with a trapped single atom in the strong coupling regime. We use a nanofiber Fabry-Perot cavity, that is, an optical nanofiber sandwiched by two fiber-Bragg-grating mirrors. Measurements of the cavity transmission spectrum with a single atom in a state-insensitive nanofiber trap clearly reveal the vacuum Rabi splitting.
Using scanning probe techniques, we show the controlled manipulation of the radiation from single dipoles. In one experiment we study the modification of the fluorescence lifetime of a single molecular dipole in front of a movable silver mirror. A second experiment demonstrates the changing plasmon spectrum of a gold nanoparticle in front of a dielectric mirror. Comparison of our data with theoretical models allows determination of the quantum efficiency of each radiating dipole.
A Single Atom in Front of a Mirror is a Universal Reservoir Computer
Wyant College of Optical Sciences, University of Arizona（亚利桑那大学怀恩特光学科学学院）；Department of Physics, University of Arizona（亚利桑那大学物理系）；School of Electrical Engineering and Telecommunications, University of New South Wales（新南威尔士大学电气工程与电信学院）
We theoretically analyze the cooling dynamics of an atom which is tightly trapped inside a high-finesse optical resonator. Cooling is achieved by suitably tailored scattering processes, in which the atomic dipole transition either scatters a cavity photon into the electromagnetic field external to the resonator, or performs a stimulated emission into the cavity mode, which then dissipates via the cavity mirrors. We identify the parameter regimes in which the atom center-of-mass motion can be cooled into the ground state of the external trap. We predict, in particular, that for high cooperativi…
We derive in the Heisenberg picture a widely used phenomenological coupling element to treat feedback effects in quantum optical platforms. Our derivation is based on a microscopic Hamiltonian, which describes the mirror-emitter dynamics based on a dielectric, a mediating fully quantized electromagnetic field, and a single two-level system in front of the dielectric. The dielectric is modeled as a a system of identical two-state atoms. The Heisenberg equation yields a system of describing differential operator equations, which we solve in the Weisskopf-Wigner limit. Due to a finite round-trip …
A novel approach to optics integration in ion traps is demonstrated based on a surface electrode ion trap that is microfabricated on top of a dielectric mirror. Additional optical losses due to fabrication are found to be as low as 80 ppm for light at 422 nm. The integrated mirror is used to demonstrate light collection from, and imaging of, a single 88 Sr+ ion trapped $169\pm4 μ$m above the mirror.
The generation of entanglement between distant atoms via single photons is the basis for networked quantum computing, a promising route to large-scale trapped-ion and trapped-atom processors. Locating the emitter within an optical cavity provides an efficient matter-light interface, but mirror-induced birefringence within the cavity introduces time-dependence to the polarisation of the photons produced. We show that such `polarisation oscillation' effects can lead to severe loss of fidelity in the context of two-photon, polarisation encoded measurement-based remote entanglement schemes. It is …
We investigate a setup where a cloud of atoms is trapped in an optical lattice potential of a standing wave laser field which is created by retro-reflection on a micro-membrane. The membrane vibrations itself realize a quantum mechanical degree of freedom. We show that the center of mass mode of atoms can be coupled to the vibrational mode of the membrane in free space, and predict a significant sympathetic cooling effect of the membrane when atoms are laser cooled. The controllability of the dissipation rate of the atomic motion gives a considerable advantage over typical optomechanical syste…
Quantum networking links quantum processors through remote entanglement for distributed quantum information processing (QIP) and secure long-range communication. Trapped ions are a leading QIP platform, having demonstrated universal small-scale processors and roadmaps for large-scale implementation. Overall rates of ion-photon entanglement generation, essential for remote trapped ion entanglement, are limited by coupling efficiency into single mode fibres5 and scaling to many ions. Here we show a microfabricated trap with integrated diffractive mirrors that couples 4.1(6)% of the fluorescence …
We investigate how superpositions of motional coherent states naturally arise in the dynamics of a two-level trapped ion coupled to the quantized field inside a cavity. We extend our considerations including a more realistic set up where the cavity is not ideal and photons may leak through its mirrors. We found that a detection of a photon outside the cavity would leave the ion in a pure state. The statistics of the ionic state still keeps some interference effects that might be observed in the weak coupling regime.
The ability to individually manipulate the increasing number of qubits is one of the many challenges towards scalable quantum information processing with trapped ions. Using micro-mirrors fabricated with micro-electromechanical systems (MEMS) technology, we focus laser beams on individual ions in a linear chain and steer the focal point in two dimensions. We demonstrate sequential single qubit gates on multiple $^{171}$Yb$^+$ qubits and characterize the gate performance using quantum state tomography. Our system features negligible crosstalk to neighboring ions ($< 3\times 10^{-4}$), and switc…
Electric-field noise due to surfaces disturbs the motion of nearby trapped ions, compromising the fidelity of gate operations that are the basis for quantum computing algorithms. We present a method that predicts the effect of dielectric materials on the ion's motion. Such dielectrics are integral components of ion traps. Quantitative agreement is found between a model with no free parameters and measurements of a trapped ion in proximity to dielectric mirrors. We expect that this approach can be used to optimize the design of ion-trap-based quantum computers and network nodes.
We report experimental observations of large Bragg reflection from arrays of cold atoms trapped near a one-dimensional nanoscale waveguide. By using an optical lattice in the evanescent field surrounding a nanofiber with a period nearly commensurate with the resonant wavelength, we observe a reflectance of up to 75% for the guided mode. Each atom behaves as a partially-reflecting mirror and an ordered chain of about 2000 atoms is sufficient to realize an efficient Bragg mirror. Measurements of the reflection spectra as a function of the lattice period and the probe polarization are reported. T…
We theoretically study the radiation-induced interaction between the mechanical motion of an oscillating mirror and a remotely trapped atomic cloud. When illuminated by continuous-wave radiation, the mirror motion will induce red and blue sideband radiation, which respectively increases and reduces motional excitation. We find that by suitably driving $Λ$-level atoms, the mirror correlation with a specific radiation sideband could be converted from the outgoing to the incoming radiation. Such process allows us to manipulate the heating and cooling effects. Particularly, we develop an optomecha…
The center-of-mass motion of optically trapped dielectric nanoparticles in vacuum is extremely well-decoupled from its environment, making a powerful tool for measurements of feeble sub-attonewton forces. We demonstrate a method to trap and manuever nanoparticles in an optical standing wave potential formed by retro-reflecting a laser beam from a metallic mirror surface. We can reliably position a $\sim 170$ nm diameter silica nanoparticle at distances of a few hundred nanometers to tens of microns from the surface of a gold-coated silicon mirror by transferring it from a single-beam tweezer t…
We investigate the Rabi oscillation of an atom placed inside a quantum cavity where each mirror is formed by a chain of atoms trapped near a one-dimensional waveguide. This proposal was studied previously with the use of Markov approximation, where the delay due to the finite travel time of light between the two cavity mirrors is neglected. We show that Rabi oscillation analogous to that obtained with high-finesse classical cavities is achieved only when this travel time is much larger than the time scale that characterizes the collective response of the atomic chain. Therefore, the delay must…
Scaling-up from prototype systems to dense arrays of ions on chip, or vast networks of ions connected by photonic channels, will require developing entirely new technologies that combine miniaturized ion trapping systems with devices to capture, transmit and detect light, while refining how ions are confined and controlled. Building a cohesive ion system from such diverse parts involves many challenges, including navigating materials incompatibilities and undesired coupling between elements. Here, we review our recent efforts to create scalable ion systems incorporating unconventional material…
We demonstrate a simple and robust geometry for optical trapping in vacuum of a single nanoparticle based on a parabolic mirror and the optical gradient force, and we demonstrate rapid parametric feedback cooling of all three motional degrees of freedom from room temperature to a few mK. A single laser at 1550nm, and a single photodiode, are used for trapping, position detection, and cooling for all three dimensions. Particles with diameters from 26nm to 160nm are trapped without feedback to 10$^{-5}$mbar and with feedback engaged the pressure is reduced to 10$^{-6}$mbar. Modifications to the …
We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is taken into account. The theory is applied to describe the scheme of a Fabry-Perot resonator with one of its mirrors moving. The friction force, as well as the diffusion, acting on the moving mirror is derived. In the limit of a small reflection coefficient, the same model provides for the description of the mechanical effect of light on an atom moving in front …
Focusing with a 4$π$ parabolic mirror allows for concentrating light from nearly the complete solid angle, whereas focusing with a single microscope objective limits the angle cone used for focusing to half solid angle at maximum. Increasing the solid angle by using deep parabolic mirrors comes at the cost of adding more complexity to the mirror's fabrication process and might introduce errors that reduce the focusing quality. To determine these errors, we experimentally examine the focusing properties of a 4$π$ parabolic mirror that was produced by single-point diamond turning. The properties…
Optomechanical systems are suitable for elucidating quantum phenomena at the macroscopic scale in the sense of the mass scale. The systems should be well-isolated from the environment to avoid classical noises, which conceal quantum signals. Optical levitation is a promising way to isolate optomechanical systems from the environment. To realize optical levitation, all degrees of freedom need to be trapped. Until now, longitudinal trapping and rotational trapping of a mirror with optical radiation pressure have been studied in detail and validated with various experiments. However, less attenti…
We consider the motion of the end mirror of a cavity in whose standing wave mode pattern atoms are trapped. The atoms and the light field strongly couple to each other because the atoms form a distributed Bragg mirror with a reflectivity that can be fairly high. We analyze how the dipole potential in which the atoms move is modified due to this backaction of the atoms. We show that the position of the atoms can become bistable. These results are of a more general nature and can be applied to any situation where atoms are trapped in an optical lattice inside a cavity and where the backaction of…
Trapped-ion (TI) quantum bits are a front-runner technology for quantum computing. TI systems with multiple interconnected traps can overcome the hardware connectivity issue inherent in superconducting qubits and can solve practical problems at scale. With a sufficient number of qubits on the horizon, the multi-programming model for Quantum Computers (QC) has been proposed where multiple users share the same QC for their computing. Multi-programming is enticing for quantum cloud providers as it can maximize device utilization, throughput, and profit for clouds. Users can also benefit from the …
Interference and coincidence detection of two photons emitted by two remote ions can lead to an entangled state which is a critical resource for scalable quantum information processing. Currently, the success probabilities of experimental realizations of this protocol are mainly limited by low coupling efficiency of a photon emitted by an ion into a single mode fiber. Here, we consider two strategies to enhance the collection probability of a photon emitted from a trapped Yb ion, using analytic methods that can be easily applied to other types of ion or neutral atoms. Our analysis shows that w…
Ordered atomic arrays trapped in the vicinity of nanoscale waveguides offer original light-matter interfaces, with applications to quantum information and quantum non-linear optics. Here, we study the decay dynamics of a single collective atomic excitation coupled to a waveguide in different configurations. The atoms are arranged as a linear array and only a segment of them is excited to a superradiant mode and emits light into the waveguide. Additional atomic chains placed on one or both sides play a passive role, either reflecting or absorbing this emission. We show that when varying the geo…
Recent progresses on quantum control of cold atoms and trapped ions in both the scientific and technological aspects greatly advance the applications in precision measurement. Thanks to the exceptional controllability and versatility of these massive quantum systems, unprecedented sensitivity has been achieved in clocks, magnetometers and interferometers based on cold atoms and ions. Besides, these systems also feature many characteristics that can be employed to facilitate the applications in different scenarios. In this review, we briefly introduce the principles of optical clocks, cold atom…
We demonstrate an optical method for detecting the mechanical oscillations of an atom with single-phonon sensitivity. The measurement signal results from the interference between the light scattered by a single trapped atomic ion and that of its mirror image. The motion of the atom modulates the interference path length and hence the photon detection rate. We detect the oscillations of the atom in the Doppler cooling limit and reconstruct average trajectories in phase space. We demonstrate single-phonon sensitivity near the ground state of motion after EIT cooling. These results could be appli…
