Macroscopic Quantum Coherence Research Articles

Entanglement and quantum coherence of two YIG spheres in a hybrid Laguerre–Gaussian cavity optomechanics

We theoretically investigate continuous variable entanglement and macroscopic quantum coherence in the hybrid L–G rotational cavity optomechanical system containing two YIG spheres. In this system, a single L–G cavity mode and both magnon modes (which are due to the collective excitation of spins in two YIG spheres) are coupled through the magnetic dipole interaction whereas the L–G cavity mode can also exchange orbital angular momentum (OAM) with the rotating mirror (RM). We study in detail the effects of various physical parameters like cavity and both magnon detunings, environment temperature, optorotational and magnon coupling strengths on the bipartite entanglement and the macroscopic quantum coherence as well. We also explore parameter regimes to achieve maximum values for both of these quantum correlations. We also observed that the parameters regime for achieving maximum bipartite entanglement is completely different from macroscopic quantum coherence. So, our present study shall provide a method to control various nonclassical quantum correlations of macroscopic objects in the hybrid L–G rotational cavity optomechanical system and have potential applications in quantum sensing, quantum meteorology, and quantum information science.

Scrutinizing the feasibility of macroscopic quantum coherence in the brain: a field-theoretical model of cortical dynamics

The neural activity patterns associated with advanced cognitive processes are characterized by a high degree of collective organization, which raises the question of whether macroscopic quantum phenomena play a significant role in cortical dynamics. In order to pursue this question and scrutinize the feasibility of macroscopic quantum coherence in the brain, a model is developed regarding the functioning of microcolumns, which are the basic functional units of the cortex. This model assumes that the operating principle of a microcolumn relies on the interaction of a pool of neurotransmitter (glutamate) molecules with the vacuum fluctuations of the electromagnetic field, termed zero-point field (ZPF). Quantitative calculations reveal that the coupling strength of the glutamate pool to the resonant ZPF modes lies in the critical regime in which the criterion for the initiation of a phase transition is fulfilled, driving the ensemble of initially independent molecules toward a coherent state and resulting in the formation of a coherence domain that extends across the full width of a microcolumn. The formation of a coherence domain turns out to be an energetically favored state shielded by a considerable energy gap that protects the collective state against thermal perturbations and entails decoherence being greatly slowed down. These findings suggest that under the special conditions encountered in cortical microcolumns the emergence of macroscopic quantum phenomena is feasible. This conclusion is further corroborated by the insight that the presence of a coherence domain gives rise to downstream effects which may be crucial for the cortical communication and the formation of large-scale activity patterns. Taken together, the presented model sheds new light on the fundamental mechanism underlying cortical dynamics and suggests that long-range synchronization in the brain results from a bottom-up orchestration process involving the ZPF.

Simulating the Interplay of Particle Conservation and Long-Range Coherence

Lasers and Bose-Einstein condensates (BECs) exhibit macroscopic quantum coherence in seemingly unrelated ways. Lasers possess a well-defined global phase while the number of photons fluctuates. InBECs of atoms, instead, the number of particles is conserved and the global phase is undefined. Here, we use gate-based quantum circuits to create a unified framework that connects lasers and BEC states. Our approach relies on a scalable circuit that measures the total number of particles without destroying long-range coherence. We introduce two complementary probes of global and relative phase coherence, study how they are affected by measurements of the particle number, and implement them on a superconducting quantum computer by Rigetti. We find that particle conservation enhances long-range phase coherence, highlighting a mechanism used by superfluids and superconductors to gain phase stiffness.

Thermodynamics of a single mesoscopic phononic mode

In recent decades, the laws of thermodynamics have been pushed down to smaller and smaller scales, within the theoretical field of stochastic thermodynamics and state-of-the-art experiments performed on microfabricated mesoscopic systems. These measurements concern thermal properties of electrons, photons, and mesoscopic mechanical objects. Here we report on the measurements of thermal fluctuations of a single mechanical mode in equilibrium with a heat reservoir. The device under study is a nanomechanical beam with a first flexural mode resonating at $3.8\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$, cooled down to temperatures in the range from 100 to $400\phantom{\rule{0.16em}{0ex}}\mathrm{mK}$. The technique is constructed around a microwave optomechanical setup using a cryogenic high electron mobility transistor, and is based on two parametric amplifications implemented in series: an in-built optomechanical ``blue detuned'' pumping plus a traveling wave parametric amplifier stage. We demonstrate our ability to resolve energy fluctuations of the mechanical mode in real time up to the fastest relevant speed given by the mechanical relaxation rate. The energy probability distribution is then exponential, matching the expected Boltzmann distribution. The variance of fluctuations is found to be ${({k}_{B}T)}^{2}$ with no free parameters. Our microwave detection floor is about three times the standard quantum limit at $6\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}$; the resolution of our fastest acquisition tracks reached about $100\phantom{\rule{0.16em}{0ex}}\mathrm{phonons}$, and is directly related to the rather poor optomechanical coupling of the device (${g}_{0}/2\ensuremath{\pi}\ensuremath{\approx}0.5\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$). This result is deeply in the classical regime, but shall be extended to the quantum case in the future with systems presenting a much larger ${g}_{0}$ (up to $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}250\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$), potentially reaching the resolution of a single mechanical quantum. We believe that it will open an experimental field, phonon-based quantum stochastic thermodynamics, with fundamental implications for quantum heat transport and macroscopic mechanical quantum coherence.

Dynamics of Bose-Einstein condensation in an asymmetric double-well potential

Josephson effect of Bose-Einstein condensate in double-well potential is an obvious manifestation of macroscopic quantum coherence. Most of researches focus on the symmetric double-well potential. In this work, we investigate the dynamic of Bose-Einstein condensates in an asymmetric double-well potential by using two-mode theory and computer simulation. In the absence of the interaction between atoms, the dynamic equation of condensate can be solved analytically. The amplitude as a function of energy difference of two wells is obtained. We can find that the change of energy difference will lead to the different dynamic behaviors of condensate. If the energy difference is relatively large, the condensate will primarily occupy the well that is occupied more than the other well at the beginning time. It is interesting that such a trap phenomenon is not dependent on the position of the high energy potential well nor the position of low energy potential well. If the energy difference becomes small, the tunneling and oscillation of condensate will be enhanced. When the interaction between atoms is present, our numerical calculations show that as the nonlinear interaction increases, the dynamic behavior of condensate exhibits different characteristics, such as trapping in a well, enhancing the tunneling and oscillation between two wells, and enhancing the trapping in a well at large nonlinear interaction, which is similar to the dynamic change caused by the energy difference in the case of ideal condensate. That is to say, on the one hand, the nonlinear interaction can lead to the trap of condensate as well as the dynamic trap to happen in symmetric double-well potential. On the other hand, the nonlinearity can promote the tunneling of condensate, counteracting the effect of the asymmetry of potential. And, this counteracting effect is related to the difference in energy between asymmetric potential wells. To understand the underlying mechanism, the full dynamic behavior of two-mode model is illustrated and the dynamic transition can be seen clearly. Combining the results obtained with and without interaction, regarding nonlinear interaction as effective potential provides a clear way to explain dynamic transition of condensate in an asymmetric double-well potential. In addition, we also perform the numerical simulations of the Gross-Pitaevskii equation, and the results are consistent with the conclusions obtained by using the two-mode theory.

Kardar-Parisi-Zhang universality in discrete two-dimensional driven-dissipative exciton polariton condensates

The statistics of the fluctuations of quantum many-body systems are highly revealing of their nature. In driven-dissipative systems displaying macroscopic quantum coherence, as exciton polariton condensates under incoherent pumping, the phase dynamics can be mapped to the stochastic Kardar-Parisi-Zhang (KPZ) equation. However, in two dimensions (2D), it was theoretically argued that the KPZ regime may be hindered by the presence of vortices, and a non-equilibrium BKT behavior was reported close to condensation threshold. We demonstrate here that, when a discretized 2D polariton system is considered, universal KPZ properties can emerge. We support our analysis by extensive numerical simulations of the discrete stochastic generalized Gross-Pitaevskii equation. We show that the first-order correlation function of the condensate exhibits stretched exponential behaviors in space and time with critical exponents characteristic of the 2D KPZ universality class, and find that the related scaling function accurately matches the KPZ theoretical one, stemming from functional Renormalization Group. We also obtain the distribution of the phase fluctuations and find that it is non-Gaussian, as expected for a KPZ stochastic process.

Skyrmion helicity: Quantization and quantum tunneling effects

We derive the quantization of magnetic helicity in the solid-state and demonstrate tunable macroscopic quantum tunneling, coherence, and oscillation for a skyrmion spin texture stabilized in frustrated magnets. We also discuss the parameter space for the experimental realization of quantum effects. Typically, for a skyrmion of 5 nm radius, quantum tunneling between two macroscopic states with distinct helicities occurs with an inverse escape rate within seconds below 100 mK, and an energy splitting in the MHz regime. Feasibility of quantum tunneling of an ensemble of magnetic spins inspires new platforms for quantum operations utilizing topologically protected chiral spin configurations.

On Macroscopic Quantum Coherence with Synchronized Atoms and Molecules: Superradiance

The collective behavior of quantum particles is one of the most intriguing phenomena in quantum optics. In particular, superradiance refers to spontaneous collective emissions from a group of quantum particles behaving collectively as a whole due to the buildup of macroscopic quantum coherence. An important question is whether macroscopic quantum coherence is constructed by means of a quantum synchronization (i.e., a quantum analog of classical synchronization) or not. The purpose of this article is to draw attention to this question from the author’s perspective. A few selected studies relevant to synchronized atoms and molecules are discussed. The author concludes that collective behaviors of quantum particles may be formulated as quantum synchronizations, but extensive studies are still needed to confirm this hypothesis.

Casimir-force-assisted ground-state cooling and macroscopic quantum coherence

We theoretically investigate the ground-state cooling and macroscopic quantum coherence of the mechanical motion in a hybrid optomechanical system with a movable cavity wall and a nearby oscillation nanosphere. In the study, the vacuum effect is used to realize a direct coupling between the movable cavity wall and the oscillation nanosphere, which plays a role in the energy transfer channel between them. We find that when the Casimir force between the mechanical oscillators is included, the ground-state cooling and the macroscopic quantum coherence of the oscillation nanosphere can be realized in a certain range of effective detuning and driving power. We discuss in detail the dependence of the quantum properties on the amplitude of Casimir force, the driving power, the optical effective detuning and the oscillation frequency of the movable mirror. The results suggest that the quantum phenomenon of a single nanosphere can be manipulated by coupling an optomechanical cavity to the nanosphere and therefore has a potential application in quantum optics and the utilization of vacuum force.

Two-site anyonic Josephson junction

Anyons are particles with intermediate quantum statistics whose wavefunction acquires a phase $e^{i\theta}$ by particle exchange. Inspired by proposals of simulating anyons using ultracold atoms trapped in optical lattices, we study a two-site anyonic Josephson junction, i.e. anyons confined in a one-dimensional double-well potential. We show, analytically and numerically, that many properties of anyonic Josephson junctions, such as Josephson frequency, imbalanced solutions, macroscopic quantum self-trapping, coherence visibility, and condensate fraction, crucially depend on the anyonic angle $\theta$. Our theoretical predictions are a solid benchmark for near future experimental quantum simulations of anyonic matter in double-well potentials.

Controlling quantum coherence and entanglement in cavity magnomechanical systems

We investigate theoretically macroscopic quantum coherence and tripartite entanglement in a three-mode magnomechanical system with a yttrium iron garnet sphere, which is simultaneously driven by a magnetic pump and a microwave field pump to establish an effective magnomechanical coupling. We discuss mainly the dependence of quantum properties on the driving power, the cavity field detuning and decay, the magnomechanical coupling strength, the bias magnetic field, and the temperature of an environment. It is found that the quantum coherence of the system can be attained easily in a large range of parameters. In contrast, tripartite photon-magnon-phonon entanglement can only be realized in a relatively small range of optical and magnetic parameters. In particular, the quantum coherence of the mechanical mode can be larger than that of the photon and magnon modes, which means that the environmental incoherence of the mechanical mode in the cavity magnomechanical system can be suppressed significantly. These results may help manipulate simultaneously the macroscopic quantum coherence and the tripartite entanglement of massive objects in coupled magnomechanical system, which may have potential applications for realizing highly tunable information processing through the flexible control of quantum properties.

Slowing quantum decoherence of oscillators by hybrid processing

Quantum information encoded into the superposition of coherent states is an illustrative representation of practical applications of macroscopic quantum coherence possessing. However, these states are very sensitive to energy loss, losing their non-classical aspects of coherence very rapidly. An available deterministic strategy to slow down this decoherence process is to apply a Gaussian squeezing transformation prior to the loss as a protective step. Here, we propose a deterministic hybrid protection scheme utilizing strong but feasible interactions with two-level ancillas immune to spontaneous emission. We verify the robustness of the scheme against the dephasing of qubit ancilla. Our scheme is applicable to complex superpositions of coherent states in many oscillators, and remarkably, the robustness to loss is enhanced with the amplitude of the coherent states. This scheme can be realized in experiments with atoms, solid-state systems, and superconducting circuits.

Universality of Dicke superradiance in arrays of quantum emitters

Dicke superradiance is an example of emergence of macroscopic quantum coherence via correlated dissipation. Starting from an initially incoherent state, a collection of excited atoms synchronizes as they decay, generating a macroscopic dipole moment and emitting a short and intense pulse of light. While well understood in cavities, superradiance remains an open problem in extended systems due to the exponential growth of complexity with atom number. Here we show that Dicke superradiance is a universal phenomenon in ordered arrays. We present a theoretical framework – which circumvents the exponential complexity of the problem – that allows us to predict the critical distance beyond which Dicke superradiance disappears. This critical distance is highly dependent on the dimensionality and atom number. Our predictions can be tested in state of the art experiments with arrays of neutral atoms, molecules, and solid-state emitters and pave the way towards understanding the role of many-body decay in quantum simulation, metrology, and lasing.

Leggett-Garg tests for macrorealism in the quantum harmonic oscillator and more general bound systems

The Leggett-Garg (LG) inequalities were introduced to test for the possible presence of macroscopic quantum coherence. Since such effects may be found in various types of macroscopic oscillators, we consider the application of the LG approach to the one-dimensional quantum harmonic oscillator and also to more general bound systems, using a single dichotomic variable $Q$ given by the sign of the oscillator position. We present a simple method to calculate the temporal correlation functions appearing in the LG inequalities for any bound system for which the eigenspectrum is (exactly or numerically) known. We apply this result to the quantum harmonic oscillator for a variety of experimentally accessible states, namely energy eigenstates, and superpositions thereof. For the subspace of states spanned by only the ground state and first excited state, we readily find substantial regions of parameter space in which the LG inequalities at two, three and four times can each be independently violated or satisfied. We also find that the violations persist, although are reduced, when the sign function defining $Q$ is smeared to reflect experimental imprecision. For higher energy eigenstates, we find that LG violations diminish, showing the expected classicalization. With a $Q$ defined using a more general type of position coarse graining, we find two-time LG violations even in the ground state. We also show that two-time LG violations in a gaussian state are readily found if the dichotomic variable at one of the times is taken to be the parity operator. To demonstrate the versatility of the approach, we repeat much of the LG analysis for the Morse potential, finding qualitatively similar physical results.

Vortex chains in rotating two-dimensional Bose-Einstein condensate in a harmonic plus optical lattices potential

<sec>Bose-Einstein condensate (BEC) is essentially a macroscopic quantum effect with quantum volatility, macroscopic quantum coherence and artificial controllability. Owing to its unique controllability, it becomes a new ideal platform for quantum simulations and studies of interacting quantum systems.</sec><sec>In this paper, the generation of vortices and the formation of vortex chains, as well as characteristics of vortex chains in rotating two-dimensional BEC in a potential composed of harmonic potential and optical lattice are studied numerically. Firstly, the generation of vortices, the formation and distribution of vortex chains and the effects of different physical parameters on the vortex chains in two-dimensional BEC are investigated by using the multigrid preconditioned conjugate gradient method. Secondly, the evolution of the vortex chains with time is studied by using the time-splitting spectral method. The results show that the generation of vortices in BEC trapped in the compound potential corresponds to the minimum value of the potential. When the depth of the optical lattice increases to a certain value, vortex chains are formed in the BEC. With the further increase of the depth of the optical lattice, the vortex depth in the vortex chain in the BEC decreases continuously, and finally the vortex chain disappears completely. When the interaction strength between atoms increases, the distribution range of the condensate expands, and the number of vortices and the number of vortex chains in the condensate also increase. When the interaction strength between atoms increases to a certain value, the symmetry of the vortex chains is broken. As the rotation frequency of the condensate increases, the distribution range of the condensate expands, and the number of vortices and the number of vortex chains in the condensate also increase. When the rotation frequency is close to the external trapping potential frequency, the linear alignment of the vortex chains is disrupted. It is also found that there are three stages in the evolution of the vortex chains in the BEC: in the first stage, vortex chains rotate together with the condensate, and the original chain distribution keeps unchanged; in the second stage, the phenomenon of vortex space extrusion appears, and the vortex chain is destroyed; in the third stage, the phenomenon of vortex space expansion occurs, and finally the vortex chains disappear. The results above show that the depth of the optical lattice, the interaction strength between atoms, and the rotation frequency of the condensate have important effects on the vortices and vortex chains in the condensate. By adjusting these physical quantities, the number of vortices and the shape of vortex chains in the BEC can be effectively manipulated. This may provide some theoretical reference and guidance for future experiments and applications.</sec>

Controlling the collective radiative decay of molecular ions in strong laser fields

Molecular ions, produced via ultrafast ionization, can be quantum emitters with the aid of resonant electronic couplings, which makes them the ideal candidates to study strong-field quantum optics. In this work, we experimentally and numerically investigate the necessary condition for observing a collective emission arising from macroscopic quantum polarization in a population-inverted N 2 + gain system, uncovering how the individual ionic emitters proceed into a coherent collection within hundreds of femtoseconds. Our results show that for a relatively high-gain case, the collective emission behaviors can be readily initiated for all the employed triggering pulse area. However, for a low-gain case, the superradiant amplification is quenched since the building time of macroscopic interionic quantum coherence exceeds the dipole dephasing time, in which situation the seed amplification and free induction decay play an essential role. These findings not only clarify the contentious key issue regarding to the amplification mechanism of N 2 + lasing but also show the unique characteristics of ultrashort laser-induced amplification in a molecular ion system where both the microscopic and macroscopic quantum coherence might be present.

Quantum Coherence Regulated by Nanoparticles in a Whispering‐Gallery‐Mode Microresonator

AbstractA theoretical investigation of the macroscopic quantum coherence in a whispering‐gallery‐mode optical microresonator is conducted, where clockwise (CW) and counterclockwise (CCW) propagating modes are coupled in nonreciprocal non‐Hermitian manner induced by nanoparticles. The results indicate that the dynamic control of quantum coherence/intercoherence can be realized by adjusting relative phase angle of the nanoparticles. A rather more exotic finding is that chiral optical quantum coherence can be achieved in the context of asymmetric backscattering. Especially in the vicinity of the exceptional point, chiral optical quantum coherence phenomenon is most obvious; that is, the CW(CCW) mode generated by backscattering exhibits strong quantum coherence while the coherence of CCW(CW) mode generated by backscattering is completely suppressed. Further, the optomechanical coherence between photons and phonons also shows chiral behavior. Finally, the experimental feasibility of quantum coherence is evaluated, and experimental scheme to readout and measure coherence is discussed briefly.

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.

High-temperature superfluorescence in methyl ammonium lead iodide

Light–matter interactions can create and manipulate collective many-body phases in solids1,2,3, which are promising for the realization of emerging quantum applications. However, in most cases, these collective quantum states are fragile, with a short decoherence and dephasing time, limiting their existence to precision tailored structures under delicate conditions such as cryogenic temperatures and/or high magnetic fields. In this work, we discovered that the archetypal hybrid perovskite, MAPbI3 thin film, exhibits such a collective coherent quantum many-body phase, namely superfluorescence, at 78 K and above. Pulsed laser excitation first creates a population of high-energy electron–hole pairs, which quickly relax to lower energy domains and then develop a macroscopic quantum coherence through spontaneous synchronization. The excitation fluence dependence of the spectroscopic features and the population kinetics in such films unambiguously confirm all the well-known characteristics of superfluorescence. These results show that the creation and manipulation of collective coherent states in hybrid perovskites can be used as the basic building blocks for quantum applications4,5.

Large spatial Schrödinger cat state using a levitated ferrimagnetic nanoparticle

The superposition principle is one of the main tenets of quantum mechanics. Despite its counter-intuitiveness, it has been experimentally verified using electrons, photons, atoms, and molecules. However, a similar experimental demonstration using a nano or a micro particle is non-existent. Here in this article, exploiting macroscopic quantum coherence and quantum tunneling, we propose an experiment using a levitated magnetic nanoparticle to demonstrate such an effect. It is shown that the spatial separation between the delocalized wavepackets of a 20 nm ferrimagnetic yttrium iron garnet (YIG) nanoparticle can be as large as 5 μm. We argue that, in addition to using for testing one of the most fundamental aspects of quantum mechanics, this scheme can simultaneously be used to test different modifications, such as wavefunction collapse models, to the standard quantum mechanics. Furthermore, we show that the spatial superposition of a core–shell structure, a YIG core and a non-magnetic silica shell, can be used to probe quantum gravity.