Macroscopic Superposition States Research Articles

Quantum Dynamics of Cavity–Bose–Einstein Condensates in a Gravitational Field

We theoretically studied the quantum dynamics of a cavity–Bose–Einstein condensate (BEC) system in a gravitational field, which is composed of a Fabry–Pérot cavity and a BEC. We also show how to deterministically generate the transient macroscopic quantum superposition states (MQSSs) of the cavity by the use of optomechanical coupling between the cavity field and the BEC. The quantum dynamics of the cavity–BEC system specifically include phase space trajectory dynamics, system excitation number dynamics, quantum entanglement dynamics, and quantum coherence dynamics. We found that the system performs increasingly complex trajectories for larger values of the Newtonian gravity parameter. Moreover, the number of phonon excitations of the system can be increased by coupling the cavity–BEC system to Newtonian gravity, which is analogous to an external direct current drive. The scattering of atoms inside the BEC affects the periodicity of the quantum dynamics of the system. We demonstrate a curious complementarity relation between the quantum entanglement and quantum coherence of cavity–BEC systems and found that the complementarity property can be sustained to some extent, despite being in the presence of the cavity decay. This phenomenon also goes some way to show that quantum entanglement and quantum coherence can be referred to together as quantum resources.

Generating macroscopic superposition states by ‎adiabatic transition

Generating macroscopic superposition states by ‎adiabatic transition

Interaction between an Optically Levitated Nanoparticle and Its Thermal Image: Internal Thermometry via Displacement Sensing.

We propose and theoretically analyze an experiment where displacement sensing of an optically levitated nanoparticle in front of a surface can be used to measure the induced dipole-dipole interaction between the nanoparticle and its thermal image. This is achieved by using a surface that is transparent to the trapping light but reflective to infrared radiation, with a reflectivity that can be time modulated. This dipole-dipole interaction relies on the thermal radiation emitted by a silica nanoparticle having sufficient temporal coherence to correlate the reflected radiation with the thermal fluctuations of the dipole. The resulting force is orders of magnitude stronger than the thermal gradient force, and it strongly depends on the internal temperature of the nanoparticle for a particle-to-surface distance greater than two micrometers. We argue that it is experimentally feasible to use displacement sensing of a levitated nanoparticle in front of a surface as an internal thermometer in ultrahigh vacuum. Experimental access to the internal physics of a levitated nanoparticle in vacuum is crucial to understanding the limitations that decoherence poses to current efforts devoted to preparing a nanoparticle in a macroscopic quantum superposition state.

Transient and Fast Generation of Bose-Einstein-Condensate Macroscopic Quantum Superposition States via Impurity Catalysing

Macroscopic quantum superposition is an important embodiment of the core of the quantum theory. The engineering of macroscopic quantum superposition states is the key to quantum communication and quantum computation. Thus, we present a theoretical proposal to engineer macroscopic quantum superposition (MQS) states of a Bose-Einstein condensate (BEC) via impurity atoms. We firstly propose a deterministic generation scheme of transient multi-component MQS states of the BEC via impurity catalysing. It is found that the structure of the generated transient multi-component MQS states can be manipulated by the impurity number parity. Then, we illustrate the influence of impurity number parity on MQS states through three aspects: generation of approximately orthogonal continuous-variable cat states, manipulation of non-classicality in phase space, and switching of non-classical degree of BEC states. The influence of the BEC decoherence on the generation of MQS states is discussed by the fidelity between actually generated states and target states. Finally, the results show that the high-fidelity multi-component MQS states of the BEC can be fast generated by increasing the coherent interaction strength between impurities and the BEC in an open system.

A brief history of Hawking's information paradox

In this invited review, we describe Hawking's information paradox and a recently proposed resolution of it. Explicit calculations demonstrate the existence of quantum hair on black holes, meaning that the quantum state of the external graviton field depends on the internal state of the black hole. Simple quantum mechanics then implies that Hawking radiation amplitudes depend on the internal state, resulting in a pure final radiation state that preserves unitarity and, importantly, violates a factorization assumption which is central to the original paradox. Black hole information is encoded in entangled macroscopic superposition states of the radiation.

Experimental violation of the Leggett-Garg inequality with a single-spin system

Investigation the boundary between quantum mechanical description and classical realistic view is of fundamental importance. The Leggett-Garg inequality provides a criterion to distinguish between quantum systems and classical systems, and can be used to prove the macroscopic superposition state. A larger upper bound of the LG function can be obtained in a multi-level system. Here, we present an experimental violation of the Leggett-Garg inequality in a three-level system using nitrogen-vacancy center in diamond by ideal negative result measurement. The experimental maximum value of Leggett-Garg function is $K_{3}^{exp}=1.625\pm0.022$ which exceeds the L\"uders bound with a $5\sigma$ level of confidence.

Robust and fast excitation fluctuations transfer between two membranes in an optomechanical system

The quantum state control or entanglement preparation for macroscopic matter is an attractive research. Optomechanical system provides an ideal platform to observe the quantum behaviors of macroscopic matter. In this paper, we present a scheme to implement the average excitation fluctuations transfer between two membranes in an optomechanical system via shortcut to adiabatic passage which is based on transitionless quantum driving. In order to quickly attain the transfer, we choose a suitable evolution path and optimize the experimental parameters. Numerical simulation demonstrates that the proposed scheme is robust against membrane damping and cavity decay. Furthermore, this idea can be used to generate entanglement of two membrane modes in a short time. Finally, we also discuss the experimental implementation of this scheme. This work may provide a new method for generating the macroscopic superposition state in the optomechanical system.

Enhancement of feasibility of macroscopic quantum superposition state with the quantum Rabi-Stark model

We propose an efficient scheme to generate a macroscopical quantum superposition state with a cavity optomechanical system, which is composed of a quantum Rabi-Stark model coupling to a mechanical oscillator. In a low-energy subspace of the Rabi-Stark model, the dressed states and then the effective Hamiltonian of the system are given. Due to the coupling of the mechanical oscillator and the atom-cavity system, if the initial state of the atom-cavity system is one of the dressed states, the mechanical oscillator will evolve into a corresponding coherent state. Thus, if the initial state of the atom-cavity system is a superposition of two dressed states, a coherent state superposition of the mechanical oscillator can be generated. The quantum coherence and their distinguishable properties of the two coherent states are exhibited by Wigner distribution. We show that the Stark term can enhance significantly the feasibility and quantum coherence of the generated macroscopic quantum superposition state of the oscillator.

Some Major Studies in Experimental Verifications of Bell Inequality

Bell inequality plays a crucial role in the debate between quantum mechanical completeness and local realism. It vigorously promoted researches on these aspects, macroscopic quantum superposition states, especially entangled states, and it has brought the debate from theory to experiment, which generated a new discipline, quantum information theory. Thus, this work briefly summarizes some major situations in the verification process of Bell inequality. At the same time, this work analyses existent some problems in the verification process of Bell inequality, and states own perception for the debate.This work can help people better understand the foundation knowledge of quantum information theory, thus quantum information theory can be applied to more actual situations.

Robust and Fast Excitation Fluctuations Transfer between Two Membranes in an Optomechanical System

The quantum state control or entanglement preparation for macroscopic matter is an attractive research. Optomechanical system provides an ideal platform to observe the quantum behaviors of macroscopic matter. In this paper, we present a scheme to implement the average excitation fluctuations transfer between two membranes in an optomechanical system via shortcut to adiabatic passage which is based on transitionless quantum driving. In order to quickly attain the transfer, we choose a suitable evolution path and optimize the experimental parameters. Numerical simulation demonstrates that the proposed scheme is robust against membrane damping and cavity decay. Furthermore, this idea can be used to generate entanglement of two membrane modes in a short time. Finally, we also discuss the experimental implementation of this scheme. This work may provide a new method for generating the macroscopic superposition state in the optomechanicalsystem.

Generating Long-Lived Macroscopically Distinct Superposition States in Atomic Ensembles.

We propose to create and stabilize long-lived macroscopic quantum superposition states in atomic ensembles. We show that using a fully quantum parametric amplifier can cause the simultaneous decay of two atoms and, in turn, create stabilized atomic Schrödinger cat states. Remarkably, even with modest parameters these intracavity atomic cat states can have an extremely long lifetime, up to 4 orders of magnitude longer than that of intracavity photonic cat states under the same parameter conditions, reaching tens of milliseconds. This lifetime of atomic cat states is ultimately limited to several seconds by extremely weak spin relaxation and thermal noise. Our work opens up a new way toward the long-standing goal of generating large-size and long-lived cat states, with immediate interests both in fundamental studies and noise-immune quantum technologies.

Coherent Interference Fringes of Two-Photon Photoluminescence in Individual Au Nanoparticles: The Critical Role of the Intermediate State.

The interaction between light and metal nanoparticles enables investigations of microscopic phenomena on nanometer length and ultrashort timescales, benefiting from strong confinement and enhancement of the optical field. However, the ultrafast dynamics of these nanoparticles are primarily investigated by multiphoton photoluminescence on picoseconds or photoemission on femtoseconds independently. Here, we presented two-photon photoluminescence (TPPL) measurements on individual Au nanobipyramids (AuNP) to reveal their ultrafast dynamics by double-pulse excitation on a global timescale ranging from subfemtosecond to tens of picoseconds. Two orders of magnitude photoluminescence enhancement, namely, coherent interference fringes, has been demonstrated. Power-dependent measurements uncovered the transform of the nonlinearity from 1 to 2 when the interpulse delay varied from tens of femtoseconds to tens of picoseconds. We proved that the real intermediate state plays a critical role in the observed phenomena, supported by numerical simulations with a three-state model. Our results provide insight into the role of intermediate states in the ultrafast dynamics of noble metal nanoparticles. The presence of the intermediate states in AuNP and the coherent control of state populations offer interesting perspectives for imaging, sensing, nanophotonics, and in particular, for preparing macroscopic superposition states at room temperature and low-power superresolution stimulated emission depletion microscopy.

Effects of local decoherence on quantum critical metrology

The diverging responses to parameter variations of systems at quantum critical points motivate schemes of quantum critical metrology (QCM), which feature sub-Heisenberg scaling of the sensitivity with the system size (e.g., the number of particles). This sensitivity enhancement by quantum criticality is rooted in the formation of Schr\"odinger cat states, or macroscopic superposition states at the quantum critical points. The cat states, however, are fragile to decoherence caused by coupling to local environments, since the local decoherence of any particle would cause the collapse of the whole cat state. Therefore, it is unclear whether the sub-Heisenberg scaling of QCM is robust against the local decoherence. Here we study the effects of local decoherence on QCM, using a one-dimensional transverse-field Ising model as a representative example. We find that the standard quantum limit is recovered by single-particle decoherence. Using renormalization group analysis, we demonstrate that the noise effects on QCM is general and applicable to many universality classes of quantum phase transitions whose low-energy excitations are described by a ${\ensuremath{\phi}}^{4}$ effective field theory. Since in general the many-body entanglement of the ground states at critical points, which is the basis of QCM, is fragile to quantum measurement by local environments, we conjecture that the recovery of the standard quantum limit by local decoherence is universal for QCM using phase transitions induced by the formation of long-range order. This work demonstrates the importance of protecting macroscopic quantum coherence for quantum sensing based on critical behaviors.

Macroscopic Superposition States in Isolated Quantum Systems

For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrodinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann's 1929 Quantum Ergodic Theorem. As a specific example, we consider a box containing a solid ball and some gas molecules. Regardless of the initial state, the system will evolve into a quantum superposition of states with the ball in macroscopically different positions. Thus, despite their seeming fragility, macroscopic superposition states are ubiquitous consequences of quantum evolution. We discuss the connection to many worlds quantum mechanics.

Generation of generalized hybrid entanglement in cavity electro–optic systems

Schrödinger’s cat paradox has revealed the entanglement between microscopic and macroscopic objects. Recently, several approaches have been proposed to generate such hybrid entangled state. In this paper, we demonstrate the generation of generalized hybrid entangled state in a cavity electro–optic system. The hybrid entangled state between the optical cavity and the microwave field is generated by a one-step evolution. Numerical simulations show that the high-fidelity entangled state is obtained even if the decay of the system is considered. Also, this proposal can be applied to generate macroscopic quantum superposition states of the microwave field.

Quantum dynamics of an impurity-doped Bose–Einstein condensate system

We study the quantum dynamics of an impurity-doped Bose–Einstein condensate (BEC) system. We show how to generate the macroscopic quantum superposition states (MQSSs) of the BEC by the use of projective measurements on impurity atoms. It is found that the nonclassicality of MQSSs can be manipulated by changing the number of the impurities and their interaction with the BEC. It is shown that the BEC matter-wave field exhibits a collapse and revival phenomenon which reveals the quantum nature of the BEC matter-wave field. We investigate the micro-macro entanglement between the impurities and the BEC, and find enhancement of the micro-macro entanglement induced by the initial quantum coherence of the impurity atoms.

Heralded Generation of Macroscopic Superposition States in a Spinor Bose-Einstein Condensate.

Macroscopic superposition states enable fundamental tests of quantum mechanics and hold a huge potential in metrology, sensing, and other quantum technologies. We propose to generate macroscopic superposition states of a large number of atoms in the ground state of a spin-1 Bose-Einstein condensate. Measuring the number of particles in one mode prepares with large probability highly entangled macroscopic superposition states in the two remaining modes. The macroscopic superposition states are heralded by the measurement outcome. Our protocol is robust under realistic conditions in current experiments, including finite adiabaticity, particle loss, and measurement uncertainty.

Criteria to detect macroscopic quantum coherence, macroscopic quantum entanglement, and an Einstein-Podolsky-Rosen paradox for macroscopic superposition states

According to classical theory, a system with two or more macroscopically distinct states available to it is in one of those states at all times. Quantum mechanics gives a different interpretation where the system can be in a superposition of such states. In this paper, we derive criteria in the form of inequalities to detect this effect, referred to as mesoscopic quantum coherence, where the states are (at least) mesoscopically distinct. Such criteria are also signatures of a mesoscopic Schr\odinger cat paradox. We extend the treatment to consider definitions and criteria for mesoscopically entangled states, which are a subset of the states exhibiting mesoscopic quantum coherence. It is shown how the criteria (referred to as type I criteria) can be applied to detect the mesoscopic entanglement of systems prepared in NOON states, Greenberger-Horne-Zeilinger states, and entangled cat states involving coherent states. Here, a larger system $C$ is entangled with a second system $S$, which can be small. The proposed definition of mesoscopic (macroscopic) entanglement involves the Schmidt decomposition, and can be applied to systems in a superposition of many states, only some pairs of which are mesoscopically (macroscopically) distinguishable. We prove that a higher-order Hillery-Zubairy entanglement criterion will detect mesoscopic entanglement of this type, and use this to demonstrate the mesoscopic entanglement of the ground state of a two-mode Bose-Einstein condensate. Finally, we explain how a subset of the type I criteria (called type II criteria) are EPR steering inequalities allowing realization of a mesoscopic or macroscopic version of the Einstein-Podolsky-Rosen paradox for macroscopic superposition states. Where the two systems $C$ and $S$ are spatially separated, we then use results from the literature to point out it is not possible to complete quantum mechanics using hidden-variable theories compatible with the assumption of locality between the two systems. The violation of certain Bell inequalities is sufficient to prove this result, which gives a stricter signature of the Schr\odinger cat paradox and of mesoscopic quantum coherence. We call such signatures type III criteria.

Macroscopic superposition states of a mechanical oscillator in an optomechanical system with quadratic coupling

We present a proposal to prepare the macroscopic superposition states of a mechanical oscillator in an optomechanical system with quadratic coupling. By coherently driving the optomechanical cavity with an external field, a Kerr-type interaction among phonons is induced. The macroscopic mechanical superposition can be generated by exploiting the Kerr nonlinearity in the mechanical oscillator, just as the generation of a nonclassical state of light in a Kerr medium. One merit of our proposal is that the Kerr nonlinearity can be strongly enhanced by adjusting the amplitude of the driving field. The influence of the system damping on the realization of mechanical non-Gaussian state is discussed by the negativity of the Wigner function. The results show that the macroscopic superposition states are robust against the mechanical thermal noise.

Symmetry-Broken Many-Body Excited States of the Gaseous Atomic Double-Well Bose-Einstein Condensate.

Macroscopic, many-body self-trapped and quantum superposition states of the gaseous double-well Bose-Einstein condensate (BEC) are investigated within the context of a multiconfigurational bosonic self-consistent field theory based upon underlying spatially symmetry-broken one-body wave functions. To aid in the interpretation of our results, an approximate model is constructed in the extreme Fock state limit, in which self-trapped and superposition states emerge in the many-body spectrum, striking a delicate balance between the degree of symmetry breaking, the effects of the condensate's mean field, and that of atomic correlation. It is found, in both the model and full theory, that the superposition state lies energetically below its related self-trapped counterpart even when many configurations are involved. Noticeably different spatial density profiles are associated with each type of excited state, thus providing a rigorous justification for approximate descriptions of high-lying excited states of the BEC.