Final Report Summary - MULTI-QG-2011 (Multidisciplinary Quantum Gravity Studies)
Summary of project objectives. A major problem of quantum field theory in curved spacetime, and quantum gravity more generally, is the lack of sufficient observational and experimental guidance. To address this issue a multidisciplinary approach towards quantum gravity was proposed, using its possible connection to easy-to-access physical systems whose description is well-established — in theory and experiment — within other fields, such as quantum information, condensed matter physics, and hydrodynamics. This allowed the candidate to address longstanding questions of semi-classical and full quantum gravity from a new perspective. In addition, the tools and concepts developed for the project’s objectives also further deepen the understanding of the non-gravitational systems evolved. In contrast to many other proposals, this programme’s objectives are both of theoretical and experimental nature, and range from a quantum information approach to quantum gravity to foundational studies on wave-current interactions.
Description of the work performed since the beginning of the project and main results achieved so far.
(I) Experimental studies.
An an experiment to study effects occurring around effective horizons in analogue gravity systems has been designed. In particular, the setup is suitable to study the Hawking and superradiant scattering processes in an analogue gravity system. To address this issue experimentally, the analogy between waves on the surface of a stationary draining fluid / superfluid flows and the behaviour of classical and quantum field excitations nearby rotating black holes has been utilized. The experimental setup has been completed, and at the beginning of 2013 experimental studies have been started. Images taken of the technical drawings and the finished setup are attached, see document ExperimentA.pdf (construction plans), ExperimentB.jpg (completed setup), and ExperimentC.jpg (effective rotating black hole/vortex flow in our setup).
(II) Theoretical studies.
Super-radiant scattering of dispersive fields. Motivated by analogue models of classical and quantum field theory in curved spacetimes and their recent experimen- tal realizations, we consider wave scattering processes of dispersive fields exhibiting two extra scattering channels. In particular, we investigate how standard super-radiant scattering processes are affected by subluminal or superluminal modifications of the dispersion relation. We analyse simple (1+1)- dimensional toy models based on fourth-order corrections to the standard second-order wave equation and show that low-frequency waves impinging on generic scattering potentials can be amplified during the process. In specific cases, by assuming a simple step potential, we determine quantitatively the deviations in the amplification spectrum that arise due to dispersion, and demonstrate that the amplification can be fur- ther enhanced due to the presence of extra scattering channels. We also consider dispersive scattering processes in which the medium where the scattering takes place is moving with respect to the observer and show that super-radiance can also be manifest in such situations.
Reducing Spacetime to Binary Information. A new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom has been presented. This is achieved by means of a binary encoding that is ergodic in the class of space-time manifolds respecting coordinate invariance of general relativity. Space-time fluctuations can be represented in a classical lattice gas model whose Boltz- mann weights are constructed with the discretized form of the Einstein-Hilbert action. Within this framework, it is possible to compute basic quantities such as the Ricci curvature tensor and the Einstein equations, and to evaluate the path integral of discrete gravity. The description as a lattice gas model also provides a novel way of quantization and, at the same time, to quantum simulation of fluctuating space-time, see document TheoryA (bit arrays and triangulations) in the attachment.
Sub-Poissonian statistics and thermalization in a quenched Bose gas. A weakly interacting homogeneous Bose gas undergoing a quench in the interaction strength has been investigated. Applying the standard Bogoliubov theory, we derive an expression for the momentum-space density-density correlation function at zero and finite temperatures. It is shown that a regime in parameter space exists for which correlations between modes of opposite momenta are enhanced over autocorrelations, a scenario equivalent to sub-Poissonian statistics. We These results are obtained by using simulations based on the truncated Wigner approximation and further show that on a time scale relevant to potential experiments that the field will thermalize with the concomitant loss of non-classical correlations. Their findings present a complete analysis of an experimentally accessible observable for non-classical behavior of fluctuations in quenched Bose gases.
Impact and knowledge utilisation.— The impact within the scientific community has partially already occurred during the funding period, intermediate scientific outputs have already been published, and if successful I expect the experimental findings to be published in high-class journals. The attempts to set up analogue gravity experiments are received with great interest within the scientific community and beyond. For example, popular science magazines, such as Nature News, “Experimental cosmology: Cosmos in a bottle”, The Economist, “Dr. Hawking’s bright idea”, the New Scientist, “Hawking radiation glimpsed in artificial black hole”, the American Institute of Physics, “Imitation Black Hole seen on Earth”, the Scientific American, “Artificial event horizon emits laboratory analogue to theoretical black hole radiation”, Physics Today, “Tabletop measurements of Hawking radiation”, APS highlights, “Making waves”, Science News, “Black Holes in the Bathtub”, have recently reported on the experimental realisation of the analogue gravity idea.
Description of the work performed since the beginning of the project and main results achieved so far.
(I) Experimental studies.
An an experiment to study effects occurring around effective horizons in analogue gravity systems has been designed. In particular, the setup is suitable to study the Hawking and superradiant scattering processes in an analogue gravity system. To address this issue experimentally, the analogy between waves on the surface of a stationary draining fluid / superfluid flows and the behaviour of classical and quantum field excitations nearby rotating black holes has been utilized. The experimental setup has been completed, and at the beginning of 2013 experimental studies have been started. Images taken of the technical drawings and the finished setup are attached, see document ExperimentA.pdf (construction plans), ExperimentB.jpg (completed setup), and ExperimentC.jpg (effective rotating black hole/vortex flow in our setup).
(II) Theoretical studies.
Super-radiant scattering of dispersive fields. Motivated by analogue models of classical and quantum field theory in curved spacetimes and their recent experimen- tal realizations, we consider wave scattering processes of dispersive fields exhibiting two extra scattering channels. In particular, we investigate how standard super-radiant scattering processes are affected by subluminal or superluminal modifications of the dispersion relation. We analyse simple (1+1)- dimensional toy models based on fourth-order corrections to the standard second-order wave equation and show that low-frequency waves impinging on generic scattering potentials can be amplified during the process. In specific cases, by assuming a simple step potential, we determine quantitatively the deviations in the amplification spectrum that arise due to dispersion, and demonstrate that the amplification can be fur- ther enhanced due to the presence of extra scattering channels. We also consider dispersive scattering processes in which the medium where the scattering takes place is moving with respect to the observer and show that super-radiance can also be manifest in such situations.
Reducing Spacetime to Binary Information. A new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom has been presented. This is achieved by means of a binary encoding that is ergodic in the class of space-time manifolds respecting coordinate invariance of general relativity. Space-time fluctuations can be represented in a classical lattice gas model whose Boltz- mann weights are constructed with the discretized form of the Einstein-Hilbert action. Within this framework, it is possible to compute basic quantities such as the Ricci curvature tensor and the Einstein equations, and to evaluate the path integral of discrete gravity. The description as a lattice gas model also provides a novel way of quantization and, at the same time, to quantum simulation of fluctuating space-time, see document TheoryA (bit arrays and triangulations) in the attachment.
Sub-Poissonian statistics and thermalization in a quenched Bose gas. A weakly interacting homogeneous Bose gas undergoing a quench in the interaction strength has been investigated. Applying the standard Bogoliubov theory, we derive an expression for the momentum-space density-density correlation function at zero and finite temperatures. It is shown that a regime in parameter space exists for which correlations between modes of opposite momenta are enhanced over autocorrelations, a scenario equivalent to sub-Poissonian statistics. We These results are obtained by using simulations based on the truncated Wigner approximation and further show that on a time scale relevant to potential experiments that the field will thermalize with the concomitant loss of non-classical correlations. Their findings present a complete analysis of an experimentally accessible observable for non-classical behavior of fluctuations in quenched Bose gases.
Impact and knowledge utilisation.— The impact within the scientific community has partially already occurred during the funding period, intermediate scientific outputs have already been published, and if successful I expect the experimental findings to be published in high-class journals. The attempts to set up analogue gravity experiments are received with great interest within the scientific community and beyond. For example, popular science magazines, such as Nature News, “Experimental cosmology: Cosmos in a bottle”, The Economist, “Dr. Hawking’s bright idea”, the New Scientist, “Hawking radiation glimpsed in artificial black hole”, the American Institute of Physics, “Imitation Black Hole seen on Earth”, the Scientific American, “Artificial event horizon emits laboratory analogue to theoretical black hole radiation”, Physics Today, “Tabletop measurements of Hawking radiation”, APS highlights, “Making waves”, Science News, “Black Holes in the Bathtub”, have recently reported on the experimental realisation of the analogue gravity idea.