Showing papers on "Quantum published in 2011"
TL;DR: In this paper, the authors give an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems, particularly focusing on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian.
Abstract: This Colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems There is particularly a focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian Several aspects of the slow dynamics in driven systems are discussed and the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions is emphasized Recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis is also reviewed and relaxation in integrable systems is discussed Finally key experiments probing quantum dynamics in cold atom systems are overviewed and put into the context of our current theoretical understanding
2,340 citations
TL;DR: In this paper, the basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field are reviewed, and the role of electron-electron interactions both in the weak coupling limit, where the electron-hole excitations are determined by collective modes, and in the strong coupling regime of partially filled relativistic Landau levels, where exotic ferromagnetic phases and incompressible quantum liquids are expected to be at the origin of recently observed (fractional) quantum Hall states.
Abstract: The basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field are reviewed. One of its most salient features is the relativistic quantum Hall effect, the observation of which has been the experimental breakthrough in identifying pseudorelativistic massless charge carriers as the low-energy excitations in graphene. The effect may be understood in terms of Landau quantization for massless Dirac fermions, which is also the theoretical basis for the understanding of more involved phenomena due to electronic interactions. The role of electron-electron interactions both in the weak-coupling limit, where the electron-hole excitations are determined by collective modes, and in the strong-coupling regime of partially filled relativistic Landau levels are presented. In the latter limit, exotic ferromagnetic phases and incompressible quantum liquids are expected to be at the origin of recently observed (fractional) quantum Hall states. Furthermore, the electron-phonon coupling in a strong magnetic field is discussed. Although the present review has a dominant theoretical character, a close connection with available experimental observation is intended.
772 citations
TL;DR: In this article, a universal quantum bound for the error in the estimation of parameters that characterize dynamical processes is derived for noisy processes, where the error is defined as a function of the number of parameters to be estimated.
Abstract: Quantum strategies can help to make parameter-estimation schemes more precise, but for noisy processes it is typically not known how large that improvement may be. Here, a universal quantum bound is derived for the error in the estimation of parameters that characterize dynamical processes.
759 citations
TL;DR: In this paper, the authors classify possible quantum phases for one-dimensional matrix product states, which represent well the class of 1D gapped ground states, and find that in the absence of any symmetry all states are equivalent to trivial product states.
Abstract: Quantum many-body systems divide into a variety of phases with very different physical properties. The questions of what kinds of phases exist and how to identify them seem hard, especially for strongly interacting systems. Here we make an attempt to answer these questions for gapped interacting quantum spin systems whose ground states are short-range correlated. Based on the local unitary equivalence relation between short-range-correlated states in the same phase, we classify possible quantum phases for one-dimensional (1D) matrix product states, which represent well the class of 1D gapped ground states. We find that in the absence of any symmetry all states are equivalent to trivial product states, which means that there is no topological order in 1D. However, if a certain symmetry is required, many phases exist with different symmetry-protected topological orders. The symmetric local unitary equivalence relation also allows us to obtain some simple results for quantum phases in higher dimensions when some symmetries are present.
719 citations
TL;DR: A criterion for quantum integrability is proposed which shows that the Rabi model is integrable due to the presence of a discrete symmetry; a generalization with no symmetries is introduced, which is the first example of a nonintegrable but exactly solvable system.
Abstract: The Rabi model is a paradigm for interacting quantum systems. It couples a bosonic mode to the smallest possible quantum model, a two-level system. I present the analytical solution which allows us to consider the question of integrability for quantum systems that do not possess a classical limit. A criterion for quantum integrability is proposed which shows that the Rabi model is integrable due to the presence of a discrete symmetry. Moreover, I introduce a generalization with no symmetries; the generalized Rabi model is the first example of a nonintegrable but exactly solvable system.
712 citations
TL;DR: The basic circuit architecture presented here provides a feasible path to ground-state cooling and subsequent coherent control and measurement of long-lived quantum states of mechanical motion and is in excellent quantitative agreement with recent theoretical predictions.
Abstract: Demonstrating and exploiting the quantum nature of macroscopic mechanical objects would help us to investigate directly the limitations of quantum-based measurements and quantum information protocols, as well as to test long-standing questions about macroscopic quantum coherence. Central to this effort is the necessity of long-lived mechanical states. Previous efforts have witnessed quantum behaviour, but for a low-quality-factor mechanical system. The field of cavity optomechanics and electromechanics, in which a high-quality-factor mechanical oscillator is parametrically coupled to an electromagnetic cavity resonance, provides a practical architecture for cooling, manipulation and detection of motion at the quantum level. One requirement is strong coupling, in which the interaction between the two systems is faster than the dissipation of energy from either system. Here, by incorporating a free-standing, flexible aluminium membrane into a lumped-element superconducting resonant cavity, we have increased the single-photon coupling strength between these two systems by more than two orders of magnitude, compared to previously obtained coupling strengths. A parametric drive tone at the difference frequency between the mechanical oscillator and the cavity resonance dramatically increases the overall coupling strength, allowing us to completely enter the quantum-enabled, strong-coupling regime. This is evidenced by a maximum normal-mode splitting of nearly six bare cavity linewidths. Spectroscopic measurements of these 'dressed states' are in excellent quantitative agreement with recent theoretical predictions. The basic circuit architecture presented here provides a feasible path to ground-state cooling and subsequent coherent control and measurement of long-lived quantum states of mechanical motion.
705 citations
TL;DR: An experiment determined the trajectories of single photons through a two-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes.
Abstract: A consequence of the quantum mechanical uncertainty principle is that one may not discuss the path or "trajectory" that a quantum particle takes, because any measurement of position irrevocably disturbs the momentum, and vice versa. Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles. We sent single photons emitted by a quantum dot through a double-slit interferometer and reconstructed these trajectories by performing a weak measurement of the photon momentum, postselected according to the result of a strong measurement of photon position in a series of planes. The results provide an observationally grounded description of the propagation of subensembles of quantum particles in a two-slit interferometer.
624 citations
TL;DR: The digital approach to quantum simulation in a system of trapped ions is demonstrated and evidence that the level of control required for a full-scale device is within reach is provided.
Abstract: A digital quantum simulator is an envisioned quantum device that can be programmed to efficiently simulate any other local system. We demonstrate and investigate the digital approach to quantum simulation in a system of trapped ions. With sequences of up to 100 gates and 6 qubits, the full time dynamics of a range of spin systems are digitally simulated. Interactions beyond those naturally present in our simulator are accurately reproduced, and quantitative bounds are provided for the overall simulation quality. Our results demonstrate the key principles of digital quantum simulation and provide evidence that the level of control required for a full-scale device is within reach.
614 citations
TL;DR: In this article, optical trapping of glass microspheres in vacuum with high oscillation frequencies, and cooling of the centre-of-mass motion from room temperature to a minimum temperature of about 1.5
Abstract: Microscale resonators cooled so that their vibrational motion approaches the quantum limit enable the study of quantum effects in macroscopic systems. An approach that could probe the interface between quantum mechanics and general relativity is now demonstrated by using lasers to suspend a glass microsphere in a vacuum. Cooling of micromechanical resonators towards the quantum mechanical ground state in their centre-of-mass motion has advanced rapidly in recent years1,2,3,4,5,6,7,8. This work is an important step towards the creation of ‘Schrodinger cats’, quantum superpositions of macroscopic observables, and the study of their destruction by decoherence. Here we report optical trapping of glass microspheres in vacuum with high oscillation frequencies, and cooling of the centre-of-mass motion from room temperature to a minimum temperature of about 1.5 mK. This new system eliminates the physical contact inherent to clamped cantilevers, and can allow ground-state cooling from room temperature9,10,11,12,13,14,15. More importantly, the optical trap can be switched off, allowing a microsphere to undergo free-fall in vacuum after cooling15. This is ideal for studying the gravitational state reduction16,17,18,19, a manifestation of the apparent conflict between general relativity and quantum mechanics16,20. A cooled optically trapped object in vacuum can also be used to search for non-Newtonian gravity forces at small scales21, measure the impact of a single air molecule14 and even produce Schrodinger cats of living organisms9.
532 citations
TL;DR: In this article, it was shown that topological features and phenomena occur not only in closed systems, but also in open quantum systems with appropriately engineered dissipation, which can make quantum systems robust to a wide class of microscopic perturbations.
Abstract: So-called topological properties can make quantum systems robust to a wide class of microscopic perturbations. Theoretical work now shows that topological features and phenomena occur not only in closed systems, but also in open quantum systems with appropriately engineered dissipation.
TL;DR: In this article, a waveguide single-photon detector based on superconducting nanowires on GaAs ridge waveguides is proposed to provide high efficiency (20%) at telecom wavelengths, high timing accuracy (60 ps), response time in the ns range, and is fully compatible with the integration of singlephoton sources, passive networks and modulators.
Abstract: The generation, manipulation and detection of quantum bits (qubits) encoded on single photons is at the heart of quantum communication and optical quantum information processing. The combination of single-photon sources, passive optical circuits and single-photon detectors enables quantum repeaters and qubit amplifiers, and also forms the basis of all-optical quantum gates and of linear-optics quantum computing. However, the monolithic integration of sources, waveguides and detectors on the same chip, as needed for scaling to meaningful number of qubits, is very challenging, and previous work on quantum photonic circuits has used external sources and detectors. Here we propose an approach to a fully-integrated quantum photonic circuit on a semiconductor chip, and demonstrate a key component of such circuit, a waveguide single-photon detector. Our detectors, based on superconducting nanowires on GaAs ridge waveguides, provide high efficiency (20%) at telecom wavelengths, high timing accuracy (60 ps), response time in the ns range, and are fully compatible with the integration of single-photon sources, passive networks and modulators.
TL;DR: In this paper, it was shown that the near-extremal solutions of EMD theories, studied in ArXiv:1005.4690, provide IR quantum critical geometries, by embedding classes of them in higher-dimensional AdS and Lifshitz solutions.
Abstract: We show that the near-extremal solutions of Einstein-Maxwell-Dilaton theories, studied in ArXiv:1005.4690, provide IR quantum critical geometries, by embedding classes of them in higher-dimensional AdS and Lifshitz solutions. This explains the scaling of their thermodynamic functions and their IR transport coefficients, the nature of their spectra, the Gubser bound, and regulates their singularities. We propose that these are the most general quantum critical IR asymptotics at finite density of EMD theories.
TL;DR: Using an interacting Bose gas of exciton-polaritons in a semiconductor microcavity, the transition from superfluidity to the hydrodynamic formation of oblique dark solitons and vortex streets in the wake of a potential barrier is reported.
Abstract: A quantum fluid passing an obstacle behaves differently from a classical one. When the flow is slow enough, the quantum gas enters a superfluid regime, and neither whirlpools nor waves form around the obstacle. For higher flow velocities, it has been predicted that the perturbation induced by the defect gives rise to the turbulent emission of quantized vortices and to the nucleation of solitons. Using an interacting Bose gas of exciton-polaritons in a semiconductor microcavity, we report the transition from superfluidity to the hydrodynamic formation of oblique dark solitons and vortex streets in the wake of a potential barrier. The direct observation of these topological excitations provides key information on the mechanisms of superflow and shows the potential of polariton condensates for quantum turbulence studies.
TL;DR: It is shown that even complex systems, with more than 1,000 internal degrees of freedom, can be prepared in quantum states that are sufficiently well isolated from their environment to avoid decoherence and to show almost perfect coherence.
Abstract: The wave nature of matter is a key ingredient of quantum physics and yet it defies our classical intuition. First proposed by Louis de Broglie a century ago, it has since been confirmed with a variety of particles from electrons up to molecules. Here we demonstrate new high-contrast quantum experiments with large and massive tailor-made organic molecules in a near-field interferometer. our experiments prove the quantum wave nature and delocalization of compounds composed of up to 430 atoms, with a maximal size of up to 60 A, masses up to m = 6,910 AMU and de Broglie wavelengths down to λdB = h/mv1 pm. We show that even complex systems, with more than 1,000 internal degrees of freedom, can be prepared in quantum states that are sufficiently well isolated from their environment to avoid decoherence and to show almost perfect coherence.
TL;DR: A fully quantum mechanical approach to describe the coupling between plasmons and excitonic systems such as molecules or quantum dots is presented, which opens a new avenue to deal with strongly interacting plasmon-excition hybrid systems.
Abstract: We present a fully quantum mechanical approach to describe the coupling between plasmons and excitonic systems such as molecules or quantum dots. The formalism relies on Zubarev's Green functions, which allow us to go beyond the perturbative regime within the internal evolution of a plasmonic nanostructure and to fully account for quantum aspects of the optical response and Fano resonances in plasmon-excition (plexcitonic) systems. We illustrate this method with two examples consisting of an exciton-supporting quantum emitter placed either in the vicinity of a single metal nanoparticle or in the gap of a nanoparticle dimer. The optical absorption of the combined emitter-dimer structure is shown to undergo dramatic changes when the emitter excitation level is tuned across the gap-plasmon resonance. Our work opens a new avenue to deal with strongly interacting plasmon-excition hybrid systems.
TL;DR: An efficient strategy for controlling a vast range of nonintegrable quantum many-body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods such as the density matrix renormalization group is presented.
Abstract: We present an efficient strategy for controlling a vast range of nonintegrable quantum many-body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods such as the density matrix renormalization group. To demonstrate its potential, we employ it to solve a major issue in current optical-lattice physics with ultracold atoms: we show how to reduce by about 2 orders of magnitude the time needed to bring a superfluid gas into a Mott insulator state, while suppressing defects by more than 1 order of magnitude as compared to current experiments [T. Stoferle et al., Phys. Rev. Lett. 92, 130403 (2004)]. Finally, we show that the optimal pulse is robust against atom number fluctuations.
TL;DR: This work investigates the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice and simulates three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk, and the first Anderson localization in a discrete quantum walk architecture.
Abstract: We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photon's wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk, and the first Anderson localization in a discrete quantum walk architecture.
TL;DR: In this paper, the authors discuss different techniques for sensitive position detection and give an overview of the cooling techniques that are being employed, including sideband cooling and active feedback cooling, and conclude with an outlook of how state-of-the-art mechanical resonators can be improved to study quantum physics.
Abstract: Mechanical systems are ideal candidates for studying quantumbehavior of macroscopic objects. To this end, a mechanical resonator has to be cooled to its ground state and its position has to be measured with great accuracy. Currently, various routes to reach these goals are being explored. In this review, we discuss different techniques for sensitive position detection and we give an overview of the cooling techniques that are being employed. The latter include sideband cooling and active feedback cooling. The basic concepts that are important when measuring on mechanical systems with high accuracy and/or at very low temperatures, such as thermal and quantum noise, linear response theory, and backaction, are explained. From this, the quantum limit on linear position detection is obtained and the sensitivities that have been achieved in recent opto and nanoelectromechanical experiments are compared to this limit. The mechanical resonators that are used in the experiments range from meter-sized gravitational wave detectors to nanomechanical systems that can only be read out using mesoscopic devices such as single-electron transistors or superconducting quantum interference devices. A special class of nanomechanical systems are bottom-up fabricated carbon-based devices, which have very high frequencies and yet a large zero-point motion, making them ideal for reaching the quantum regime. The mechanics of some of the different mechanical systems at the nanoscale is studied. We conclude this review with an outlook of how state-of-the-art mechanical resonators can be improved to study quantum {\it mechanics}.
TL;DR: It is found that superposition and entanglement are sustained in this living system for at least tens of microseconds, exceeding the durations achieved in the best comparable man-made molecular systems.
Abstract: In artificial systems, quantum superposition and entanglement typically decay rapidly unless cryogenic temperatures are used. Could life have evolved to exploit such delicate phenomena? Certain migratory birds have the ability to sense very subtle variations in Earth's magnetic field. Here we apply quantum information theory and the widely accepted "radical pair" model to analyze recent experimental observations of the avian compass. We find that superposition and entanglement are sustained in this living system for at least tens of microseconds, exceeding the durations achieved in the best comparable man-made molecular systems. This conclusion is starkly at variance with the view that life is too "warm and wet" for such quantum phenomena to endure.
TL;DR: In this paper, the authors derived a master equation that takes into account the qubit-resonator coupling and showed that the failure of the quantum optical master equation is manifest in the ultrastrong coupling regime.
Abstract: Cavity and circuit QED study light-matter interaction at its most fundamental level. Yet, this interaction is most often neglected when considering the coupling of this system with an environment. In this paper, we show how this simplification, which leads to the standard quantum optics master equation, is at the root of unphysical effects. Including qubit relaxation and dephasing, and cavity relaxation, we derive a master equation that takes into account the qubit-resonator coupling. Special attention is given to the ultrastrong coupling regime, where the failure of the quantum optical master equation is manifest. In this situation, our model predicts an asymmetry in the vacuum Rabi splitting that could be used to probe dephasing noise at unexplored frequencies. We also show how fluctuations in the qubit frequency can cause sideband transitions, squeezing, and Casimir-like photon generation.
TL;DR: In this paper, the Hamiltonian parameters of Yb2Ti2O7 were extracted from high-field inelastic neutron scattering experiments and shown to support a Coulombic ground state in low magnetic fields and host an unusual quantum critical point at larger fields.
Abstract: Recent work has highlighted remarkable effects of classical thermal fluctuations in the dipolar spin ice compounds, such as ‘‘artificial magnetostatics,’’ manifesting as Coulombic power-law spin correlations and particles behaving as diffusive ‘‘magnetic monopoles.’’ In this paper, we address quantum spin ice, giving a unifying framework for the study of magnetism of a large class of magnetic compounds with the pyrochlore structure, and, in particular, discuss Yb2Ti2O7, and extract its full set of Hamiltonian parameters from high-field inelastic neutron scattering experiments. We show that fluctuations in Yb2Ti2O7 are strong, and that the Hamiltonian may support a Coulombic ‘‘quantum spin liquid’’ ground state in low magnetic fields and host an unusual quantum critical point at larger fields. This appears consistent with puzzling features seen in prior experiments on Yb2Ti2O7. Thus, Yb2Ti2O7 is the first quantum spin liquid candidate for which the Hamiltonian is quantitatively known.
TL;DR: In this article, a brief review discusses electronic properties of mesoscopic graphene-based structures, including edges, nanoribbons, quantum dots, pn-junctions, pnp-structures, and quantum barriers and waveguides.
TL;DR: In this paper, a nano-sized structure was proposed to achieve an optimal conversion of heat flow to directed current by quantization of energy levels and the physics of single charge Coulomb interaction.
Abstract: We present a microscopic discussion of a nano-sized structure which uses the quantization of energy levels and the physics of single charge Coulomb interaction to achieve an optimal conversion of heat flow to directed current. In our structure the quantization of energy levels and the Coulomb blockade lead to the transfer of quantized packets of energy from a hot source into an electric conductor to which it is capacitively coupled. The fluctuation-generated transfer of a single energy quantum translates into the directed motion of a single electron. Thus in our structure the ratio of the charge current to the heat current is determined by the ratio of the charge quantum to the energy quantum. An important novel aspect of our approach is that the direction of energy flow and the direction of electron motion are decoupled.
TL;DR: In this article, the authors introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties, including symmetry-breaking and critical phenomena, in the simpler setting of Monte Carlo studies of classical spin systems.
Abstract: These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of Monte Carlo studies of classical spin systems, to illustrate finite-size scaling at continuous and first-order phase transitions. Exact diagonalization and quantum Monte Carlo (stochastic series expansion) algorithms and their computer implementations are then discussed in detail. Applications of the methods are illustrated by results for some of the most essential models in quantum magnetism, such as the S=1/2 Heisenberg antiferromagnet in one and two dimensions, as well as extended models useful for studying quantum phase transitions between antiferromagnetic and magnetically disordered states.
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20 Apr 2011
TL;DR: In this paper, a non-orthodox version of Quantum Theory and the need for von Neumann's Process are discussed. But the authors do not discuss the relationship between quantum physics and neuroscience.
Abstract: Science and Human Values.- Human Knowledge as the Foundation Science.- Actions, Knowledge, and Information.- Nerve Terminals and the Need to Use Quantum Theory.- Templates for Action.- The Physical Effectiveness of Conscious Will.- Support from Contemporary Psychology.- Application to Neuropsychology.- Roger Penrose's Theory and Quantum Decoherence.- Faster-Than-Light Connections.- Whiteheadian Quantum Ontology.- An Interview.- Consciousness and the Anthropic Questions.- Impact of Quantum Mechanics on Human Values.- Conclusions.- Appendices.- Non-orthodox Versions of Quantum Theory and the Need for von Neumann's Process.- The Basis Problem in Many- Worlds Theories.- Despised Dualism.- Recent Views in Neuroscience and Philosophy.- Gazzaniga's "The Ethical Brain".- Von Neumann: Knowledge, Information, and Entropy.- Wigner's Friend and Consciousness in Quantum Physics.- Orthodox Interpretation and the Mind-Brain Connection.- Einstein Locality and Spooky Action at a Distance.- Locality in Physics.- Nonlocality in Quantum Physics.
TL;DR: Experimental evidence is provided that interaction between the bacteriochlorophyll chromophores and the protein environment surrounding them not only prolongs quantum coherence, but also spawns reversible, oscillatory energy transfer among excited states.
Abstract: The photosynthetic light-harvesting apparatus moves energy from absorbed photons to the reaction center with remarkable quantum efficiency. Recently, long-lived quantum coherence has been proposed to influence efficiency and robustness of photosynthetic energy transfer in light-harvesting antennae. The quantum aspect of these dynamics has generated great interest both because of the possibility for efficient long-range energy transfer and because biology is typically considered to operate entirely in the classical regime. Yet, experiments to date show only that coherence persists long enough that it can influence dynamics, but they have not directly shown that coherence does influence energy transfer. Here, we provide experimental evidence that interaction between the bacteriochlorophyll chromophores and the protein environment surrounding them not only prolongs quantum coherence, but also spawns reversible, oscillatory energy transfer among excited states. Using two-dimensional electronic spectroscopy, we observe oscillatory excited-state populations demonstrating that quantum transport of energy occurs in biological systems. The observed population oscillation suggests that these light-harvesting antennae trade energy reversibly between the protein and the chromophores. Resolving design principles evident in this biological antenna could provide inspiration for new solar energy applications.
TL;DR: In this paper, it was shown that the near-extremal solutions of EMD theories, studied in arXiv:1005.4690, provide IR quantum critical geometries, by embedding classes of them in higher dimensional AdS and Lifshitz solutions.
Abstract: We show that the near-extremal solutions of Einstein-Maxwell-Dilaton theories, studied in arXiv:1005.4690, provide IR quantum critical geometries, by embedding classes of them in higher-dimensional AdS and Lifshitz solutions. This explains the scaling of their thermodynamic functions and their IR transport coefficients, the nature of their spectra, the Gubser bound, and regulates their singularities. We propose that these are the most general quantum critical IR asymptotics at finite density of EMD theories.
TL;DR: This work implements direct controllable coupling between quantized mechanical oscillators held in separate locations through the mutual Coulomb interaction of two ions held in trapping potentials separated by 40 μm, establishing that direct coherent motional coupling is possible for separately trapped ions.
Abstract: The harmonic oscillator is a simple and ubiquitous physical system, and various oscillators functioning at the quantum mechanical level are known. Previously, linkage between two quantum mechanical oscillators has been achieved only indirectly, but two groups now demonstrate direct coupling at the quantum level between two harmonic oscillators in separate locations. Such systems could be used as the building blocks for quantum information processors and simulators. Brown et al. achieve direct controllable coupling between 9Be+ ions held 40 micrometres apart in trapping potentials. In a similar experiment, Harlander et al. couple single 40Ca+ ions trapped 54 μm apart. In their system, additional ions act as antennae to amplify the coupling. The harmonic oscillator is a simple and ubiquitous physical system. This paper reports a new realization in the quantum regime, achieving direct controllable coupling between quantized mechanical oscillators. The oscillators are ions held in trapping potentials (separated by 40 micrometres) and coupled through their mutual Coulomb interaction. The system could be used as a building block for quantum computers and simulators. The harmonic oscillator is one of the simplest physical systems but also one of the most fundamental. It is ubiquitous in nature, often serving as an approximation for a more complicated system or as a building block in larger models. Realizations of harmonic oscillators in the quantum regime include electromagnetic fields in a cavity1,2,3 and the mechanical modes of a trapped atom4 or macroscopic solid5. Quantized interaction between two motional modes of an individual trapped ion has been achieved by coupling through optical fields6, and entangled motion of two ions in separate locations has been accomplished indirectly through their internal states7. However, direct controllable coupling between quantized mechanical oscillators held in separate locations has not been realized previously. Here we implement such coupling through the mutual Coulomb interaction of two ions held in trapping potentials separated by 40 μm (similar work is reported in a related paper8). By tuning the confining wells into resonance, energy is exchanged between the ions at the quantum level, establishing that direct coherent motional coupling is possible for separately trapped ions. The system demonstrates a building block for quantum information processing and quantum simulation. More broadly, this work is a natural precursor to experiments in hybrid quantum systems, such as coupling a trapped ion to a quantized macroscopic mechanical or electrical oscillator9,10,11,12,13.
TL;DR: In this article, the requirements to test some of the most paradigmatic collapse models with a protocol that prepares quantum superpositions of massive objects are analyzed in a general framework and taking into account only unavoidable sources of decoherence: blackbody radiation and scattering of environmental particles.
Abstract: We analyze the requirements to test some of the most paradigmatic collapse models with a protocol that prepares quantum superpositions of massive objects. This consists of coherently expanding the wave function of a ground-state-cooled mechanical resonator, performing a squared position measurement that acts as a double slit, and observing interference after further evolution. The analysis is performed in a general framework and takes into account only unavoidable sources of decoherence: blackbody radiation and scattering of environmental particles. We also discuss the limitations imposed by the experimental implementation of this protocol using cavity quantum optomechanics with levitating dielectric nanospheres.