Gravitational generation of quantum entanglement on squeezed coherent states in a system of two quantum mechanical particles is explored. The particles are modeled as harmonic oscillators, and their gravitational interaction is described by an interaction potential. Dynamics of the gravi- tationally induced entanglement is explored using the linear entropy of entanglement. An analytical expression for the linear entropy is obtained via Gaussian integration and covariance method. In the short-time weakly coupled regime, it is observed that the entanglement is proportional to the square of the time interval, square of the interaction strength, and proportional to the squeezing parameters of the modes. These results provide insights into the effects of quantum squeezing on entanglement generation in systems with gravitational interactions. Analytically and numerically it is shown that momentum squeezing can enhance gravitationally induced quantum entanglement.
Gravitational generation of quantum entanglement on squeezed coherent states in a system of two quantum mechanical particles is explored. The particles are modeled as harmonic oscillators, and their gravitational interaction is described by an interaction potential. Dynamics of the gravi- tationally induced entanglement is explored using the linear entropy of entanglement. An analytical expression for the linear entropy is obtained via Gaussian integration and covariance method. In the short-time weakly coupled regime, it is observed that the entanglement is proportional to the square of the time interval, square of the interaction strength, and proportional to the squeezing parameters of the modes. These results provide insights into the effects of quantum squeezing on entanglement generation in systems with gravitational interactions. Analytically and numerically it is shown that momentum squeezing can enhance gravitationally induced quantum entanglement.
Gravitationally induced entanglement has been proposed as a probe of the quantum nature of gravity. This work analyzes a system of two particles in harmonic traps interacting only through gravity, considering thermal and two-mode squeezed initial states. For thermal states, a maximum temperature is identified above which entanglement cannot be generated, and for fixed system parameters an optimal trap frequency that maximizes the logarithmic negativity is found. Squeezing the initial state does not further enhance the entanglement generation, but increases the temperature range over which it can be observed. Extending the analysis to general Gaussian states, an upper bound on the achievable entanglement is derived and shown to be saturated, for example, by ground and squeezed states. The results show that the amount of entanglement generated in this setup is extremely small, highlighting the experimental challenges of observing gravitationally induced quantum effects.
We investigate gravitationally generated entanglement in two quantum harmonic oscillators induced by quadratic (Stelle) gravity, including corrections up to 1.5 post-Newtonian order. Starting from the quadratic action, we derive the effective two-body Hamiltonian for two harmonically trapped masses, incorporating the contributions of the massive spin-2 ghost (m2) and massive spin-0 (m0) degrees of freedom of the gravitational field. For two quantised oscillators prepared in their ground state, we compute the von Neumann and Rényi entropies of the reduced state and identify a frequency at which the gravitationally-induced entanglement vanishes due to cancellation between relativistic momentum squeezing and quantum-delocalisation-induced position squeezing. We further analyze the cancellation frequency and derive the approximate constraint m0<34m2 for the spin-2 and spin-0 modes. This relation follows from demanding a stable harmonic oscillator description. Finally, we study gravitationally-induced concurrence in a non-Gaussian setup and show how quadratic gravity modifies the entanglement generated between two spatial superpositions. The concurrence can approach O(1) for certain choices of mass, spatial superposition, particle distance, and spin-2 and spin-0 modes. The concurrence will deviate from Newtonian gravity at certain particle separations, depending on the energy of the spin-2 and spin-0 modes. For example, spin modes as low as 0.0197 eV become distinguishable from Newtonian gravity at a distance d∼40μm. This allows us to constrain the spin-2 and spin-0 masses in experiments.
In this paper, we investigate into the numerical and analytical relationship between the dynamically generated quadrature squeezing and entanglement within a coupled harmonic oscillator system. The dynamical relation between these two quantum features is observed to vary monotically, such that an enhancement in entanglement is attained at a fixed squeezing for a larger coupling constant. Surprisingly, the maximum attainable values of these two quantum entities are found to consistently equal to the squeezing and entanglement of the system ground state. In addition, we demonstrate that the inclusion of a small anharmonic perturbation has the effect of modifying the squeezing versus entanglement relation into a nonunique form and also extending the maximum squeezing to a value beyond the system ground state.
Abstract No experiment to date has provided evidence for quantum features of the gravitational interaction. Recently proposed tests suggest looking for the generation of quantum entanglement between massive objects as a possible route towards the observation of such features. Motivated by advances in optical cooling of mirrors, here we provide a systematic study of entanglement between two masses that are coupled gravitationally. We first consider the masses trapped at all times in harmonic potentials (optomechanics) and then the masses released from the traps. This leads to the estimate of the experimental parameters required for the observation of gravitationally induced entanglement. The optomechanical setup demands LIGO-like mirrors and squeezing or long coherence times, but the released masses can be light and accumulate detectable entanglement in a timescale shorter than their coherence times. No macroscopic quantum superposition develops during the evolution. We discuss the implications from such thought experiments regarding the nature of the gravitational coupling.
Quantum walk is a synonym for multi-path interference and spread of particle in superposition of position space. We study the effects of a quantum mechanical interaction modeled to mimic quantum mechanical gravitational interaction between the two states of the walkers. The study has been carried out to investigate the entanglement generation between the two quantum walkers that do not otherwise interact. We see that the states do in fact get entangled more and more as the quantum walks unfold. We investigate the dependence of this entanglement generation on the coin parameter of the walks. With the introduction of noise into the dynamics, we also show the sensitivity of entanglement entropy between the two walkers on the noise introduced in one of the walks.
We investigate the dynamical enhancement of entanglement by means of local squeezing of initial separable Gaussian states in two coupled harmonic oscillator systems. Interestingly, the maximum generation of entanglement between the two modes is not a monotonically increasing function of the squeezing parameter. Instead, there exists a critical degree of squeezing r c for the maximum entanglement to be enhanced. For the coupled oscillator systems considered, we have derived the analytical expressions of r c .