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The deflection of light in the gravitational field of the Sun is one of the most fundamental consequences for general relativity as well as one of its classical tests first performed by Eddington a century ago. However, despite its centre stage role in modern physics, no experiment has tested it in an ostensibly quantum regime where both matter and light exhibit nonclassical features. This paper shows that the interaction which gives rise to the light-bending also induces photon-matter entanglement as long as gravity and matter are treated at par with quantum mechanics. The quantum light-bending interaction within the framework of perturbative quantum gravity highlights this point by showing that the entangled states can be generated already with coherent states of light and matter exploiting the nonlinear coupling induced by graviton exchange.
The primary principle used in the paper is that, if gravity were a quantum mediator, it could generate entanglement - we calculate the linearized entropy assuming such a quantum gravitational interaction. Furthermore, we suggest and perform a viability analysis of a tabletop experiment to detect said entropy changes.
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Figure from [1].
Schematic setup of the scattering problem and QBF. P denotes the observer and λ radius of the event horizon. Ψ_T(x) is the superposed incident wave function going into black hole. (Image from [1])
Plot of the probability current J(x,t=0) as a function of observer distance x. Classically one would not expect a positive current - marked in red (since the incident wavefunction had a negative velocity). (Image from [1])
Quantum backflow across a black hole horizon in a toy model approach (2021)
Quantum backflow across a black hole horizon in a toy model approach (2021)
Quantum backflow, discovered quite a few years back, is a generic, purely quantum phenomenon, in which the probability of finding a particle (as given by its wavefunction) in a direction is nonzero (and increasing for a certain period of time) even when the particle has with certainty, a velocity in the opposite direction. In this project, we studied the QBF component of a wave packet by investigating the scattering across the event horizon of a Schwarzschild black hole. In a toy model approach (since our constructed wave function is not normalisable, yet!), we consider a superposition of two ingoing solutions and observe the probability density and probability current [1]. We explicitly demonstrate a nonvanishing quantum back flow in a small region around the event horizon. This is in contrast to the classical black hole picture in which, once an excitation crosses the horizon, it is lost forever from the outside world. Deeper implications of this phenomenon are speculated. We also study quantum backflow for another spacetime with horizon, the Rindler spacetime, where the phenomenon can be studied only within the Rindler wedge. Although quantum scattering problems involving point particles and black holes have been investigated in detail (see [2] for example), our novelty lies in explicitly showing a non-zero backflow, when (classical) logic dictates otherwise.
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Quantum Mechanics of a Particle on a Torus Knot: Curvature and Torsion Effects (2019)
Quantum Mechanics of a Particle on a Torus Knot: Curvature and Torsion Effects (2019)
In this project, we calculated the eigenvalues and eigenfunctions of a point particle moving on a non-planar curve lying on the surface of a torus, formally known as the torus knot. Our approach involved finding the geometric potential (this typically depends on the curvature and torsion of the curve) which constrained the particle to move on the torus knot, instead of R3, and using it as the potential in the time-independent Schrödinger equation (TISE). Our results indicated corrections to a previous computation by Sreedhar V. V. [1]. In particular, we found that even in the thin-torus limit, the energy eigenvalues depend on the winding number of the torus knot [2] (which is also a unique identifier for a particular knot).
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Left: a surface plot showing the un-normalised ground-state eigenfunction ψ(η,ϕ). Right: two slices of the surface plot for η=1.5 and η=6. The sinusoidal nature is more pronounced for η=6, as expected for torus knots with large aspect ratio η. (Image from [2])
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