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Conference Full Paper Template Acceleration Radiation from a Quantum Optical Perspective Marlan Scully Texas A&M, Princeton, and Baylor Universities ABSTRACT The interface between quantum optics and general relativity has a rich history and a promising future. Indeed, quantum optical scientist Gerry Moore (of our group) in his famous Ph.D. thesis [1] was the first to show that accelerating the mirrors of an optical cavity produced photons. In this and the next three talks (Ordoñez, Svidzinsky, and Azizi), we will discuss: • A quantum optical approach to radiation from atoms falling into, e.g., a Schwarzschild [2] and Kerr [3] black hole with special attention to Einstein’s equivalence principle. • We will also present our results on causality in acceleration radiation studied by considering the joint probability of an accelerated atom emitting a photon and a photodetector fixed in space registering a count. This simple model yields insight into counterintuitive issues associated with causality, vacuum entanglement, and related topics. • We also find that Unruh acceleration from the negative frequency perspective yields interesting results [5]. For example, a photon emitted by an accelerated ground state atom cannot be absorbed by another ground state atom accelerated in the same direction, but it can be absorbed by an atom accelerated in the opposite direction. References [1] G. Moore, J. Math. Phys., 11, 2679 (1970) – rejected by Physical Review. [2] Scully, M., Fulling, S., Lee, D., Page, D., Schleich, W., Svidzinsky, A., Quantum optics approach to radiation from atoms falling into a black hole, PNAS, 201807703, (2018) [3] A. Azizi, H. E. Camblong, A. Chakraborty, C. R. Ordonez, and M. O. Scully, Acceleration radiation of an atom freely falling into a Kerr black hole and near-horizon conformal quantum mechanics, arXiv:2011.08368 [4] M. Scully, A. Svidzinsky, and W. G. Unruh, Phys. Rev. Res., 1, 033115 (2019) [5] A. Svidzinsky, A. Azizi, J. Ben-Benjamin, M. Scully, and W. Unruh, TBP. Unruh and Cherenkov radiation from a negative frequency perspective and causality in quantum optics Anatoly Svidzinsky1, Arash Azizi1, Marlan O. Scully1,2,3 and William Unruh4 1Texas A&M University, 2Baylor, 3Princeton, 4University of British Columbia A ground-state atom uniformly accelerated through the Minkowski vacuum can become excited by emitting an Unruh-Minkowski photon. We show that from the perspective of an accelerated atom, the sign of the frequency of the Unruh-Minkowski photons can be positive or negative depending on the acceleration direction. The accelerated atom becomes excited by emitting an Unruh-Minkowski photon which has negative frequency in the atom’s frame, and decays by emitting a positive frequency photon. This leads to interesting effects. For example, the photon emitted by accelerated ground-state atom can not be absorbed by another ground-state atom accelerating in the same direction, but it can be absorbed by an excited atom or a ground-state atom accelerated in the opposite direction (see Fig. 1a). We also show that similar effects take place for Cherenkov radiation. Namely, a Cherenkov photon emitted by an atom can not be absorbed by another ground-state atom moving with the same velocity, but can be absorbed by an excited atom or a ground-state atom moving in the opposite direction. Emission of photons by atoms can occur into modes which extend into a region causally disconnected with the emitter. For example, a uniformly accelerated ground-state atom emits a photon into Unruh- Minkowski mode which is exponentially larger in the causally disconnected region [1]. This makes an impression that photon emission is acausal. We show that conventional quantum optical analysis yields that a detector atom will not detect the emitted photon in the region non-causally connected with the emitter. For example, if the interaction between the fixed detector atom 2 and the field is turned on and off adiabatically (see Fig. 1b) then atom 2 gets excited only if it is causally connected with the emitting atom 1. Figure 1: (a) Trajectory of atoms uniformly accelerated in different Rindler wedges. (b) Atom 1 accelerates from −∞ to +∞ along hyperbolic trajectory. Unruh acceleration radiation from atom 1 is shown as a wavy line which is absorbed by the fixed detector atom 2. [1] W.G. Unruh and R.M. Wald, What happens when an accelerating observer detects a Rindler particle, Phys. Rev. D 29, 1047 (1984). The event horizon and the logarithmic phase singularity in the inverted harmonic oscillator F. Ullinger1,∗, M. Zimmermann1,2, M.A. Efremov1,2, W.P. Schleich1,2,3, G.G. Rozenman4,5, L. Shemer6 and A. Arie5 1Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQST ), Universität Ulm, Ulm, Germany 2Institute of Quantum Technologies, German Aerospace Center (DLR), Ulm, Germany 3Hagler Institute for Advanced Study at Texas A&M University, Texas A&M AgriLife Research, Institute for Quantum Science and Engineering (IQSE), and Department of Physics and Astronomy, Texas A&M University, College Station, USA 4Raymond and Beverly Sackler School of Physics & Astronomy, Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel 5School of Electrical Engineering, Iby and Aladar Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel 6School of Mechanical Engineering, Iby and Aladar Fleischman Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel ∗[email protected] When atoms fall into a black hole, they emit acceleration radiation [1], which resembles the Hawking radiation [2] for a distant observer. Close to the event horizon the corresponding wave displays a logarithmic phase singularity. In this talk, we investigate the appearance of similar effects in a simple quantum system, namely an one-dimensional inverted harmonic oscillator. In fact, the Wigner function corresponding to an energy eigenfunction of the inverted harmonic oscillator [3,4], as depicted in Fig. 1, clearly displays an event horizon in phase space. Although usually hidden, even a logarithmic phase singularity in combination with an amplitude singularity emerges if the system is viewed from the right angle. Fig. 1: Phase space representation of an energy eigenstate of the inverted harmonic oscillator with the dimensionless energy = 0.4. Here, the diagonal from the bottom left to the top right resembles an event horizon for an incoming particle from the right. Revealing the event horizon and the singularities in phase and amplitude for a wave function, requires a transformation of the energy eigenstates. For this purpose, we propagate these particular states (i) in the presence of a harmonic oscillator and (ii) in the absence of a potential. Then, at very particular times, the event horizon and the logarithmic phase singularity become visible. These fascinating effects might, for instance, be observable with surface gravity water waves, an analogue system to quantum mechanics which allows amplitude and phase measurements [5] enabling the reconstruction of the Wigner function. [1] M. O. Scully, S. Fulling, D. M. Lee, D. N. Page, W. P. Schleich, and A. A. Svidzinsky, Quantum optics approach to radiation from atoms falling into a black hole, Proceedings of the National Academy of Sciences 115, 8131 (2018). [2] S. W. Hawking, Black hole explosions?, Nature 248, 30 (1974). [3] N. L. Balazs and A. Voros, Wigner’s function and tunneling, Annals of Physics 199, 123 (1990). [4] D. M. Heim, W. P. Schleich, P. M. Alsing, J. P. Dahl, and S. Varro, Tunneling of an energy eigenstate through a parabolic barrier viewed from Wigner phase space, Physics Letters A 377, 1822 (2013). [5] G. Rozenman, S. Fu, A. Arie, and L. Shemer, Quantum mechanical and optical analogies in surface gravity water waves, Fluids 4, 96 (2019). Black Holes in Phase Space and Logarithmic Phase Singularity in Surface Gravity Water Waves Gary G. Rozenman1*, Freyja Ullinger3, Lev Shemer2, Matthias Zimmermann3, Maxim A. Efremov3, Wolfgang P. Schleich3,4, and Ady Arie1 1 Dept. of Physical Electronics, Faculty of Engineering, Tel-Aviv University, Tel-Aviv 6997801, Israel 2 School of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, Tel-Aviv 6997801, Israel 3 Institut für Quantenphysik and Center for Integrated Quantum Science and Technology, Universität Ulm, 89081 Ulm, Germany 4 Hagler Institute for Advanced Study at Texas A&M University, Texas A&M AgriLife Research, Institute for Quantum Science and Engineering (IQSE), and Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USA In classical mechanics, a massive point-like particle accelerates in a linear potential. Within the quantum-mechanical description, the wave function corresponding to this particle accumulates a position-dependent phase, associated with the momentum change in the linear potential, as well as a position-independent Kennard phase that scales with the third power of time (푡3) during which the particle experienced the linear potential [1]. Since 1927, this cubic phase has emerged in various physical phenomena [2]. However, although being a fundamental property of quantum mechanics, so far, no direct observation of the Kennard phase has been reported, since any setup providing us only with the probability density is insensitive to any global position- independent phase. In many aspects, the time evolution of a wave function in quantum mechanics is analogous to that of surface gravity water wave pulses. Hence, we utilized this analogy and studied for the first time the propagation of surface gravity water waves in an effective linear potential, realized by means of a time-dependent homogeneous and well-controlled water flow. In our experiments, we have measured the cubic phase, for the first time for both Gaussian and Airy wave packets [3,4]. Interestingly, these experiments also allowed to open a new window to a study of ballistic dynamics of wave packets and accelerating solitary wave packets [5]. Inspired by these successful experiments, we extend this analogy to a study of electromagnetic fields around black holes and different types of phase singularities, including a logarithmic phase singularity.
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