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.
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.
Abstract 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.
A description of the dynamical response of uniformly trapped Bose–Einstein condensates (BECs) to oscillating external gravitational fields is developed, with the inclusion of damping. Two different effects that can lead to the creation of phonons in the BEC are identified; direct driving and parametric driving. Additionally, the oscillating gravitational field couples phonon modes, which can lead to the transition of excitations between modes. The special case of the gravitational field of a small, oscillating sphere located closely to the BEC is considered. It is shown that measurement of the effects may be possible for oscillating source masses down to the milligram scale, with a signal to noise ratio of the order of 10. To this end, noise terms and variations of experimental parameters are discussed and generic experimental parameters are given for specific atom species. The results of this article suggest the utility of BECs as sensors for the gravitational field of very small oscillating objects which may help pave the way towards gravity experiments with masses in the quantum regime.
The field of cavity optomechanics is based on the coupling of optical cavities to mechanical degrees of freedom. Over the past two decades, it has led to remarkable and surprising discoveries. A cavity optomechanical system enabled the first observation of gravitational waves, a discovery awarded with the 2017 Nobel prize, confirming Einstein's 100-year-old prediction. It was also a cavity optomechanical system that has for the first time enabled ground state cooling of the motion of an object containing ~1012 atoms, and entanglement of mechanical oscillators of similar size. Moreover, cavity optomechanical systems have facilitated significant progress in precision-sensing technologies, with diverse applications such as biosensing, magnetometry, and many more.But this may only be the beginning. The field is still in its early days and experimental capabilities are improving fast. For instance, cavity optomechanical systems have the potential to test predicted signatures of quantum gravity such as modifications to the canonical commutator, short-distance modifications to Newtonian gravity, dark matter and dark energy, and even extra dimensions. In this sense, they form an economical platform with a short experimental turnover time, that can compete in its predictive power with mega-scale, multi-billion-dollar experiments such as the Large Hadron Collider.This thesis is dedicated to utilizing cavity optomechanics to explore the maybe most challenging and unexplored frontier in quantum mechanics: The dynamics of macroscopic quantum systems. Quantum physics, since its discovery in the early 20th century, has revolutionized our understanding of the microworld, but has long been thought to apply exclusively to extremely small objects. However, over the past decades, ever-larger quantum systems have emerged in laboratories around the world. On one hand, these are collective, macroscopic quantum phenomena such as superfluidity, superconductivity, and Bose-Einstein condensation. On the other hand, they are quantum states of relatively massive mechanical objects. While our understanding of the interplay of quantum mechanical and classical systems has greatly improved over the past decades, as described by theories of decoherence and open quantum systems, many basic questions about macroscopic quantum systems still remain unanswered. Quantum fluids such as Bose-Einstein condensates and superfluid helium are inherently hard to understand due to their complex dynamics, and difficult to probe experimentally due to the weakness of their interactions with the environment and their fragile nature. This is especially true in the strongly-interacting regime, which is, for instance, found in superfluid helium.Another long-standing, unanswered set of questions in quantum mechanics is related to the quantum measurement problem. What constitutes a quantum measurement? What happens if we engineer a quantum state that is large enough to be, in principle, part of our everyday world? What if we attempt to create a quantum superposition of a living being? Do the laws of physics even permit either of these scenarios?Cavity optomechanics is a unique and powerful platform to investigate macroscopic quantum systems. The extreme sensitivity of cavity optomechanical sensors in readout of mechanical motion makes them susceptible to minute quantum effects. The strong coupling between single photons and phonons in these systems allows engineering and measurement of quantum states of mechanical systems. Furthermore, most cavity optomechanical experiments are cryo-compatible and small in size, which allows integration with other quantum systems to be analyzed, such as superfluid helium.
We present a theoretical interacting one-dimensional Bose-Einstein condensate (BEC) inside an optical cavity which is driven through of the fixed end mirrors. Under the Bogoliubov approximation and when the number of photons inside the cavity is not too large, the atomic field operator can be considered as a single-mode quantum field which is coupled to the radiation pressure of the intracavity field. In this way, the system behaves like an optomechanical system with an extra nonlinear term corresponding to the atom-atom interaction.We show that one of the best ways of tracing the effect of atomic interaction is to study the noise power spectrum of the field of the cavity. For this purpose, we study the light intensity spectrum of the cavity as well as the entanglement between the optical cavity and the BEC. We show how the pattern of the power spectrum of the cavity changes due to the nonlinear effect of atomic collisions. Furthermore, it is shown that due to the s-wave scattering frequency of the atom-atom interaction, one can measure the strength of interatomic interaction. Besides, we show how the atomic collisions affect the entanglement between subsystems and cooling behavior of the BEC atoms.
This dissertation contains a study of ultracold atoms in optical cavities. We particularly focus on two aspects of the coupled atom-cavity systems. In the first aspect, we implement the quantum nature of the light field to probe the quantum state of the atoms. This is interesting due to the nondestructive nature of the characterization of many-body atomic states. In the second aspect we study the cavity optomechanics that investigates the coupling of mechanical and optical degrees of freedom via radiation pressure. The optomechanical cavity provides an interesting nonlinear system to study the coupling between atoms and the intracavity field.In the context of cavity quantum electrodynamics we study the reflection of two counter-propagating modes of the light field in a high-Q ring cavity by ultracold atoms either in the Mott insulator state or in the superfluid state of an optical lattice. We find that the dynamics of the reflected light strongly depends on both the lattice spacing and the state of the matter-wave field. By using the Monte Carlo wave-function method to account for the cavity damping we also determine the two-time correlation function and the time-dependent physical spectrum of theretroreflected field. We find that the light field and the atoms become entangled if the latter are in a superfluid state. We also analyze quantitatively the entanglement between the atoms and the light.In cavity optomechanics the mechanical effect can either comes from a vibrating macroscopic oscillator or a collective density excitation of a Bose-Einstein condensate. First we use a Fabry-Perot-type cavity to study the opto-mechanically-induced bistable quantum phase transitions between superfluid and a Mott insulator states of an ultracold bosonic gases trapped inside the cavity. Secondly, we study the symmetricand antisymmetric collective density side modes of the BEC which results from the optomechanical effects of the light fields in a ring cavity.
Abstract We extend our earlier work [1] on probing a gravitational cat state (gravcat) to the quantum superposition of two gravcats in an exemplary model and in Bose–Einstein condensates (BEC). In addition to its basic theoretical values in gravitational quantum physics and macroscopic quantum phenomena, this investigation can provide some theoretical support to experimental proposals for measuring gravity-induced entanglement and the quantum nature of perturbative gravity. In the first part we consider cat states generated by double-well potentials. A pair of gravcats, each approximated as a two-level system, is characterized by gravity - induced Rabi oscillations , and by gravity - induced entanglement of its energy eigenstates. In the second part we turn to a (non-relativistic) quantum field theory description and derive a gravitational Gross – Pitaevsky equation for gravcats formed in BEC. Using a mathematical analogy to quantum rotors, we explore the properties of the two-gravcat system for BECs, its physical consequences and observational possibilities. Finally we discuss our results in comparison to predictions of alternative quantum theories, and we explain their implications.