Acceleration from a Quantum Optical Perspective

Marlan Scully Texas A&M, Princeton, and Baylor Universities

ABSTRACT

The interface between quantum optics and 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] with special attention to Einstein’s . • 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 registering a count. This simple model yields insight into counterintuitive issues associated with causality, 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 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 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 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 [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 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. In my talk, I explain in detail the analogy between surface gravity water waves and the Schrödinger equation, including the Fig. 2: Amplitude of a propagating Gaussian wave transformation from the Schrödinger equation to that of an packet in an inverted harmonic potential electromagnetic field around a black hole. In addition, I will show preliminary results of the emulation of electromagnetic fields around the gravity of a black hole and logarithmic phase singularities.

*Corresponding Author’s Email: [email protected] [1] E. H. Kennard, Zur Quantenmechanik einfacher Bewegungstypen, Zeitschrift für Physik, 44, 326 (1927). [2] M. Zimmermann et al. T3 -Interferometer for atoms, Appl. Phys. B, 123:102 (2017). [3] G. G. Rozenman et al. Amplitude and Phase of Wavepackets in Linear Potential, 122, 124302, Phys. Rev. Lett. (2019). [4] G. G. Rozenman et al. Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves, Fluids, 4(2), 96 (2019). [5] G. G. Rozenman et al. Observation of Accelerating Solitary Wavepackets, Phys. Rev. E. 101, 050201(R) (2020)

Franco Nori RIKEN, Saitama, Japan; and the University of Michigan, Ann Arbor, USA

Theoretical prediction and subsequent observation of the dynamical in a superconducting circuit.

We theoretically investigated [1-5] the dynamical Casimir effect (DCE) in electrical circuits based on superconducting microfabricated waveguides with tunable boundary conditions. We proposed implementing a rapid modulation of the boundary conditions by tuning the applied magnetic flux through superconducting quantum-interference devices that are embedded in the waveguide circuits. We considered two circuits: (i) An open waveguide circuit that corresponds to a single mirror in free space, and (ii) a resonator coupled to a microfabricated waveguide, which corresponds to a single-sided cavity in free space. We analyzed the properties of the DCE in these two setups by calculating the generated photon-flux densities, output-field correlation functions, and the quadrature squeezing spectra. We showed that these properties of the output field exhibit signatures unique to the radiation due to the DCE, and could, therefore, be used for distinguishing the DCE from other types of radiation in these circuits. We also discussed the similarities and differences between the DCE, in the resonator setup, and the down-conversion of pump photons in parametric oscillators.

We observed [2] the dynamical Casimir effect in a superconducting circuit consisting of a coplanar transmission line with a tunable electrical length. The rate of change of the electrical length can be made very fast (a substantial fraction of the speed of ) by modulating the inductance of a superconducting quantum interference device at high frequencies (>10 gigahertz). In addition to observing the creation of real photons, we detected two-mode squeezing in the emitted radiation, which is a signature of the quantum character of the generation process.

The pedagogical overview [4] covers this and other related effects (Hawking, Unruh, ...).

1. J.R. Johansson, G. Johansson, C.M. Wilson, F. Nori, Dynamical Casimir effect in a superconducting coplanar waveguide, Phys. Rev. Lett. 103, 147003 (2009). [PDF][Link][arXiv]. Featured in Physics, Editors' Suggestion

2. J.R. Johansson, G. Johansson, C.M. Wilson, F. Nori, Dynamical Casimir effect in superconducting circuits, Phys. Rev. A 82, 052509 (2010). [PDF][Link][arXiv]

3. C.M. Wilson, G. Johansson, A. Pourkabirian, J.R. Johansson, T. Duty, F. Nori, P. Delsing, Observation of the dynamical Casimir effect in a superconducting circuit, Nature 479, 376-379 (2011). [PDF][Link][arXiv]. The supplementary material is here [PDF][Link]. Featured in a Nature "News & Views" [PDF][Link]. Physics World top five Physics breakthroughs of the year 2011 [PDF][Link]. According to Nature, coverage of our work on Nature News was "The most read news story of 2011". [PDF][Link]

4. P.D. Nation, J.R. Johansson, M.P. Blencowe, F. Nori, Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits, Rev. Mod. Phys. 84, 1-24 (2012). [PDF][Link][arXiv]

5. J.R. Johansson, G. Johansson, C.M. Wilson, P. Delsing, F. Nori, Nonclassical microwave radiation from the dynamical Casimir effect, Phys. Rev. A 87, 043804 (2013). [PDF][Link][arXiv]

PDF files of our publications are available via this URL link: https://dml.riken.jp/pub/

Dynamical Casimir Effect: fully quantum-mechanical and non-perturbative description of

both the cavity field and the oscillating mirror

Salvatore Savasta, University of Messina, Italy,

Abstract: This talk will provide a brief summary of some recent developments on the theory of the Dynamical Casimir Effect [1-4]. This effect was studied in optomechanical systems by using a fully quantum-mechanical and non-perturbative description of both the cavity field and the oscillating mirror [1]. Within this approach, we showed that the resonant generation of photons from the vacuum is determined by a ladder of mirror- field vacuum Rabi splittings. Moreover, we showed that vacuum emission can originate from the free evolution of an initial pure mechanical excited state, in analogy with the spontaneous emission from excited atoms [1,2].

This study also shows that a resonant production of photons out of the vacuum can be observed even for mechanical frequencies lower than the cavity-mode frequency [1]. I will also present results on the quantification of the entanglement between the oscillating mirror and the radiation produced by its motion in the vacuum field. Finally, I will show how virtual photon pairs can mediate the coherent interaction of mechanical oscillators [3].

Reference:

1. V. Macrì, A. Ridolfo, O. Di Stefano, A.F. Kockum, F. Nori, S. Savasta, Nonperturbative Dynamical Casimir Effect in Optomechanical Systems: Vacuum Casimir-Rabi Splittings, Phys. Rev. X 8, 011031 (2018). [PDF][Link][arXiv]

2. A. Settineri, V. Macrì, L. Garziano, O. Di Stefano, F. Nori, S. Savasta, Conversion of mechanical noise into correlated photon pairs: Dynamical Casimir effect from an incoherent mechanical drive, Phys. Rev. A 100, 022501 (2019). [PDF][Link][arXiv]

3. O. Di Stefano, A. Settineri, V. Macrì, A. Ridolfo, R. Stassi, A.F. Kockum, S. Savasta, F. Nori, Interaction of Mechanical Oscillators Mediated by the Exchange of Virtual Photon Pairs, Phys. Rev. Lett. 122, 030402 (2019). [PDF][Link][arXiv][Suppl. Info.]

4. W. Qin, V. Macrì, A. Miranowicz, S. Savasta, F. Nori, Emission of photon pairs by mechanical stimulation of the squeezed vacuum, Phys. Rev. A 100, 062501 (2019). [PDF][Link][arXiv]

Tunneling and the logarithmic phase singularity

Wolfgang P. Schleich

Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, D-89069 Ulm; Institute of Quantum Technologies, German Aerospace Center (DLR), D-89081 Ulm, Germany; Hagler Institute for Advanced Study, Department of Physics and Astronomy and Institute for Quantum Science and Engineering (IQSE), Texas A&M University, College Station, TX 77843, USA

The formulation of quantum mechanics in terms of the Wigner phase space distribution function [1] is particularly useful since it brings out most clearly the characteristic features of quantum theory such as interference. In this way it also allows us to distinguish quantum from classical noise.

In this talk we briefly summarize important properties of the Wigner function and then use this tool to analyze the tunneling [2] of a particle through a repulsive potential resulting from an inverted harmonic oscillator.

We point out the existence of an event horizon in phase space resulting from the Sommerfeld radiation condition and giving birth to a logarithmic phase singularity. In particular, we connect the behavior of the Wigner function of an energy eigenstate of the inverted oscillator shown in Fig. 1 to this phase singularity.

Figure 1 The Wigner function of an energy eigenstate of the inverted harmonic oscillator for an energy below the top of the barrier and corresponding to a particle coming from the left.

References

[1] W.P. Schleich, Quantum Optics in Phase Space (VCH-Wiley, Weinheim, 2001).

[2] 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, Phys. Lett. A 377, 1822-1825 (2013). Arash Azizi

Unruh Radiation and Causality

Texas A&M University, College Station, TX 77843, USA Email: [email protected]

ABSTRACT

Quantum field theory (QFT) in the curved space-time yields intriguing results due to the existence of different vacua. Hawking radiation and Unruh effect are two main examples. QFT in Minkowski background respects the notion of causality, however, when acceleration and gravity has been considered, one needs to be careful. We address the issue of causality by a study of two uniformly accelerated two-level atoms in two different scenarios: the same and opposite directions of accelerations (i.e. atoms reside in the same and opposite Rindler wedges). We found the Vacuum-to-vacuum probability amplitude of initial ground states and final excited states of atoms to be vanished in the former case and to be non-zero in the latter; counter intuitive result from a Minkowski observer, but a natural result from a Rindler one. We also found, as we expect from the Unruh-Wald 1984 result, the correlation function is exponentially larger in the opposite wedge scenario than that of the same wedge. The above statement is not contradictory with causality and can be justified by the fact that the Minkowski vacuum is a maximally entangled state between the Rindler right and left wedges. Michael J. Duff

Embedding black holes in higher dimensions or yet another derivation of the Hawking

Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ, United Kingdom; IQSE, Texas A&M University, College Station, TX 77843, USA Email: m.duff@imperial.ac.uk

ABSTRACT

We derive the Hawking temperature of the Schwarzschild black hole by requiring that the embedding of the black hole in higher dimensions be regular in Euclidean signature (following Fronsdal’s work in lorentzian signature). We also consider generalisations to the Reissner-Nordstrom and Kerr-Newman cases. (Unpublished work with Chris Pope).

2 Stephen A. Fulling

What Is Still to be Learned about Classical Acceleration Radiation?

Texas A&M University, College Station, TX 77843, USA Email: [email protected]

ABSTRACT

The Unruh problem (a uniformly accelerated detector of field quanta) has much in common with the old problem of a uniformly accelerated charge (or scalar source), some aspects of which are still surprisingly controversial. (1) Does a uniformly accelerated charge radiate at all? Which is more fundamental, the Larmor radiation formula or the Abraham- Lorentz-Dirac radiation reaction formula? (2) Is a classical point charge even meaningful (as distinct from a continuous charge distribution)? If not, what is the classical limit of the Dirac equation? (3) Equivalence principle conundrums: A uniformly accelerated charge does not radiate as seen by a coaccelerated observer. Does such an observer see a stationary charge radiate? Does a charge at rest on a table radiate to a freely falling observer? The search for an international professional consensus on such issues and their quantum correlates is the subject of an ongoing Internet discussion group and a special issue in progress of the journal Symmetry.

3 Atsushi Higuchi

The Unruh effect in interacting scalar field theory

Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK Email: [email protected]

ABSTRACT

The Minkowski vacuum state is the so-called purified KMS state with respect to the Rindler energy in free field theory. This state is a thermal state if it is restricted to a Rindler wedge (the Unruh effect). This fact has been shown also in interacting field theories satisfying the Wightman axioms. I outline how it can be shown in perturbation theory for scalar field theory using the Euclidean formulation. A similar argument can be applied to other static with bifurcate Killing horizons such as Schwarzschild and de Sitter spacetimes. (This is a joint work in progress with William C C de Lima.)

4 Eduardo Martin-Martinez

The Unruh effect in slow motion

Institute for Quantum Computing, University of Waterloo, Waterloo, ON, N2L 3G1, Canada; Dept. Applied Math., University of Waterloo, Waterloo, ON, N2L 3G1, Canada; Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada Email: [email protected]

ABSTRACT

We show under what conditions an accelerated detector (e.g., an atom/ion/molecule) thermalizes while interacting with the vacuum state of a quantum field in a setup where the detector’s acceleration alternates sign across multiple optical cavities. We show (non- perturbatively) in what regimes the probe “forgets” that it is traversing cavities and ther- malizes to a temperature proportional to its acceleration. Then we analyze in detail how this thermalization relates to the renowned Unruh effect. Finally, we use these results to propose an experimental testbed for the direct detection of the Unruh effect at relatively low probe speeds and accelerations, potentially orders of magnitude below previous proposals.

5 George Matsas

On the observability of the Unruh effect in the laboratory

Institute for Theoretical Physics/ S˜aoPaulo State University, Brazil Email: [email protected]

ABSTRACT

On the one hand, the Unruh effect is as well tested as quantum field theory itself. On the other one, the Unruh effect is quite nonintuitive still raising confusion. This drives us to the observability issue. After a fast review about what the Unruh effect is and is not, we argue that a general strategy for observing the Unruh effect must (i) analyze some phenomenon with respect to Rindler observers in the Rindler wedge using the Unruh thermal bath, (ii) translate the corresponding results in terms of what inertial observers should see in the lab, and (iii) confirm this experimentally. We finish claiming that classical Larmor radiation satisfies conditions (i)-(iii) making it eligible to be considered one such an observation.

6 Carlos Ord´o˜nez

Near-horizon conformal aspects of acceleration radiation detected by a two-level atom freely falling into static or rotating black holes

Department of Physics, University of Houston, Houston, Texas 77024 USA; Department of Physics and Astronomy, Rice University, MS 61, 6100 Main Street, Houston, Texas 77005, USA Email: [email protected]

ABSTRACT

A two-level atom freely falling towards a Schwarzschild black hole was recently shown to detect radiation in the Boulware vacuum in an insightful paper [M. O. Scully et al., Proc. Natl. Acad. Sci. U.S.A. 115, 8131 (2018)]. The two-state atom acts as a dipole detector and its interaction with the field can be modeled using a quantum optics approach. The relative acceleration between the scalar field and the detector causes the atom to detect the radiation. I will describe in this talk how this acceleration radiation is driven by the near-horizon physics of the black hole. This insight reinforces the relevance of near-horizon conformal quantum mechanics for all the physics associated with the thermodynamic prop- erties of the black hole. We additionally highlight the conformal aspects of the radiation that is given by a Planck distribution with the Hawking temperature. Our approach allows us to handle more general geometries and initial conditions than in the above reference, as well as the important case of Kerr black holes, confirming in all cases the results by Scully et al. My emphasis will be on the basic ideas and logic of the calculation, rather than on the mathematical details.

7 Christopher N. Pope

Black Holes, The Gibbs Surface and Negative

George P. & Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX 77843, USA; DAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 OWA, UK Email: [email protected]

ABSTRACT

A spacetime with more than one Killing horizon, such as a charged or rotating black hole, has negative as well as positive surface gravities on the different horizons. Usually, they are all assigned a positive Hawking temperature, although the resulting first law of thermody- namics then takes on a non-standard form. We show that it is more natural to associate negative surface gravity with negative temperature. Not only does the first law become the standard one, but it also accords with the Gibbsian viewpoint of thermodynamics, where the temperature is defined from the Gibbs surface. It also accords with a microscopic D-brane explanation of the black hole thermodynamics, with the temperatures for the left-moving and right-moving modes both being positive, as they must be for a physically-meaningful statistical description.

8 Jeff Steinhauer

Spontaneous Hawking radiation and beyond: Observing the time evolution of an analogue black hole

Technion – Israel Institute of Technology Email: jeff[email protected]

ABSTRACT

We confirm the stationary character of the spontaneous Hawking radiation in an ana- logue black hole. Furthermore, we follow the time evolution of the Hawking radiation, and compare and contrast it with the predictions for real black holes. We observe the ramp up of the Hawking radiation, similar to a real black hole. The end of the spontaneous Hawking radiation is marked by the formation of an inner horizon. The Maryland group predicted that particles emanating from the inner horizon can cause stimulated Hawking radiation. We find that these stimulated Hawking pairs are directly observable.

9 William G. Unruh

Measurement of Acceleration Radiation in BEC Analogue system

University of British Columbia, Canada; Texas A&M University, College Station, TX 77843, USA Email: [email protected]

ABSTRACT

Given the intimate connection of gravity and its dependence on the changing flow of time from place to place, it is surprizing that General Relativistic effects can be modeled in other systems. In 1981 I showed that even the Hawking effect has analogies in other systems, which has spawned an active experimental effort in the past few decades. A harder case has turned out to to model the thermal effect that an accelerated detector in the vacuum sees. Following Bell and Leinaas in 1983, a group of us have shown that a circularly accelerated detector can also show a themal effect. This talks will present a way of implimenting a broad band detector of the quantum fluctuations in a BEC which may also be just realisable with an interferometric detector by borrowing techniques from LIGO, but with the interferometer operating in frequency space rather than in real space.

10 Robert Wald

The Particle and Energy Cost of Entanglement of Hawking Radiation with the Final Vacuum State

Kavli Institute for Cosmological Physics and Enrico Fermi Institute,The University of Chicago, Chicago, IL 60637, USA; Department of Physics, The University of Chicago, Chicago, IL 60637, USA Email: [email protected]

ABSTRACT

A semiclassical analysis shows that in the process of black hole formation and evapora- tion, an initial pure state will evolve to a mixed state, i.e., information will be lost. One way of avoiding this conclusion without invoking drastic modifications of the local laws of physics in a low curvature regime would be for the information to be restored at the very end of the evaporation process. Hotta, Schutzhold, and Unruh have analyzed a (1 + 1)- dimensional moving mirror analog of the Hawking process and have found that, in this model, information is restored via entanglement of the early time Hawking radiation with vacuum fluctuations in the spacetime region to the future of the event where the mirror re- turns to inertial motion. We analyze their model here and give a precise formulation of this entanglement by introducing the notion of “Milne particles.” We then analyze the inertial particle and energy cost of such an entanglement of Hawking radiation with vacuum fluctu- ations. We show that that, in fact, the entanglement of early time Hawking radiation with vacuum fluctuations requires the emission of at least as many late time inertial particles as Hawking particles. Although the energy cost can be made small in the (1 + 1)-dimensional mirror system, this should not be the case for the (3 + 1)-dimensional evaporating black hole system. Thus, vacuum entanglement has the same difficulties as the more usual burst scenarios for attempting to avoid information loss.

11 Silke Weinfurtner

Quantum simulators for fundamental physics

The University of Nottingham, UK Email: [email protected]

ABSTRACT

Analogue gravity summarises an effort to mimic physical processes that occur in the interplay between general relativity and field theory in a controlled laboratory environment. The aim is to provide insights in phenomena that would otherwise elude observation: when gravitational interactions are strong, when quantum effects are important, and/or on length scales that stretch far beyond the observable . The most promising analogue gravity systems up-to-date are fluids, superfluids, ultra-cold atoms and optical systems. I will discuss recent efforts to explore the quantum origin of the Universe and rotating black hole physics in the laboratory.

12