Quantum coherence, radiance, and resistance of gravitational systems

We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A systematic approach to the generation of gravitational waves in the quantum domain is presented that recovers known classical limits in terms of the quadrupole radiation formula and backreaction dissipation. Classical gravitational emission and absorption relations are quantized into their quantum field theoretical counterparts in terms of the corresponding operators and quantum ensemble averages. Certain arising consistency issues related to factor ordering have been addressed and resolved. Using the theoretical formulation established here with numerical simulations in the quantum regime, we discuss potential new effects including decoherence through the spontaneous emission of gravitons and collectively amplified radiation of gravitational waves by correlated quantum particles.

Figure 1

Plots (a)–(c) show the simulation of the symmetric modulus of the density matrix $|{\rho }_{p,p^{\prime }}|(t)$ for $p,p^{\prime }=1,2,\dots 56$ consisting of even harmonic modes for the quantum transitions through the superradiance of gravitational waves. Five scalar bosons in a harmonic trap are initially in the same highest energy state at the top right corner of the density matrix, where all 5 particles occupy the harmonic mode $n=6$. While releasing a short burst of gravitational wave, they spontaneously decay towards the ground state in the bottom left corner, where all 5 particles occupy the $n=0$ mode. Plot (d) shows the average radiation power per particle as a function of time for a similar initial state as in plots (a)–(c) but with different particle numbers.

Figure 2

Plots (a)–(c) show the simulation of $|{\rho }_{p,p^{\prime }}|(t)$. Here 5 scalar bosons in a harmonic trap are initially equally distributed along the diagonal of the density matrix for harmonic modes $n=0$, 2, 4, 6 as a maximally mixed state. While releasing a continuously decreasing gravitational wave, they spontaneously decay toward the ground state in the bottom left corner, where all 5 particles occupy the $n=0$ mode. Plot (d) shows the average radiation power per particle for a similar initial state with different particle numbers.

Figure 3

Plots (a)–(c) show the simulation of $|{\rho }_{p,p^{\prime }}|(t)$. Here, 5 scalar bosons in a harmonic trap are initially equally and fully distributed in the density matrix for harmonic modes $n=0$, 2, 4, 6 as a maximally entangled state. While releasing a continuously decreasing gravitational wave, they spontaneously decay toward the ground state in the bottom left corner, where all 5 particles occupy the $n=0$ mode. Plot (d) shows the average radiation power per particle for a similar initial state with different particle numbers.