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arXiv:1103.4838 · Complexity

Experimental evidence for mixed reality states

Alfred W. Hubler, Vadas Gintautas

Published May 28, 2008• 3 citations
arXivHTMLPDF

Abstract

ecently researchers at the University of Illinois coupled a real pendulum to its virtual counterpart.They observed that the two pendulums suddenly start to move in synchrony if their lengths are sufficiently close [1].In this synchronized state, the boundary between the real system and the virtual system is blurred, that is, the pendulums are in a mixed reality state.An instantaneous, bidirectional coupling is a prerequisite for mixed reality states.In the experimental setup, a motor moves the pivot point of the real pendulum slightly whenever the virtual pendulum moves, and vice versa.This requires a fast probe, a fast motor controller, and a fast computer that can run the virtual pendulum in real time and accomplish the communication between the probe and the motor controller.When a real system is coupled to its virtual counterpart with a small, bidirectional, instantaneous coupling, the coupled system is an interreality system.A phase transition separates the two states of an interreality system: a dual reality state and a mixed reality state.In a mixed reality state, (i) the motion of the real system and the motion of the virtual system are in step and synchronized; (ii) the energy of the entire system is conserved; (iii) the amplitude of the motion increases to a large limiting amplitude; (iv) the real system strengthens the motion of the virtual system and vice versa; and thus (v) the interreality system can generate a large output signal.In a dual reality state, (i) the motion of the real system and the motion of the virtual system are out of step and not synchronized; (ii) if the energy loss due to friction is negligible, the energy of the real system and the virtual system are conserved separately; (iii) the amplitude of the motion decreases; (iv) the real system does not strengthen the motion of the virtual system and vice versa; and (v) the interreality system cannot generate a large output signal (see Figure 1).Synchronization between two real systems has been studied extensively in the past [2].For example, in a laser the dynamics of the electrons of different molecules can synchronize and thus produce a laser pulse of high intensity.Synchronization between real systems can be exploited for desirable effects.Lasers are used in CD players, laser pointers, and as energy efficient light sources.However, synchronization can also lead to destruction and catastrophes.At the opening of the Millennium Bridge in London to pedestrian traffic, the bridge started to sway sideways, which in turn caused the pedestrians to walk in step with the motion of In a mixed reality state, the motion of the real system and the motion of the virtual system are in step.

DOI
10.1002/cplx.20234

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This thesis provides a fundamental characterization of photon gases in nanostructured microcavities, investigating the underlying physics that may eventually support new forms of information processing. While the transition from electronic to photonic architectures is often motivated by the physical limits of semiconductors, such as the ’power wall’ and carrier scattering, realizing these systems requires a deep understanding of quantum dynamics. This work addresses these fundamental questions by examining collective dynamics in condensate networks, single-particle tunneling, and the thermodynamics of isolated quantum gases. The first part of this work explored the collective behavior of coupled photon Bose-Einstein condensates as a preliminary step toward building larger computational networks. By experimentally realizing a negatively coupled triplet of condensates, this study demonstrated that the system resides in a frustrated state. Although this represents only a fundamental building block, it serves as a necessary milestone for the potential scaling of these networks into larger Hamiltonian simulators. Future research in this direction will be required to implement reconfigurable coupling geometries and to determine if these analog systems can effectively compete with classical heuristic algorithms for complex optimization tasks. The second part of this research was the investigation of particle motion within classically forbidden regions. Understanding the transport mechanisms that govern phase coherence is essential for any platform where particles must move between defined sites. Using a measurement scheme based on two coupled waveguides, where population transfer acts as a clock to determine particle speed, evanescent states in a reflective potential step were analyzed. The results revealed an inverse relationship between energy and speed, where lower energy leads to higher speeds within the potential. These findings agree with the Büttiker and Landauer tunneling time framework, suggesting that the effective speed within the barrier is governed by the interaction between phase and amplitude gradients. Extending this waveguide clock methodology to more complex landscapes, such as periodic barriers or time-dependent potentials, will clarify the role of amplitude gradients in particle transport. This understanding directly supports the design of high-speed quantum electronic components, where evanescent states play a major role. The final section examined the emergence of thermodynamic behavior from an isolated quantum system. This was achieved by studying a photon gas within a gravitational wedge billiard. Experimental analysis of spatial autocorrelation functions showed that the microcanonical standard deviation decreases as the system approaches the semiclassical limit, which supports the Eigenstate Thermalization Hypothesis. Furthermore, thermodynamic phase transitions in the microcanonical density of states, surface entropy, and surface temperature were observed. Because the gas is two-dimensional, these transitions were driven entirely by the geometry of the billiard. The quantum virial theorem was also qualitatively confirmed. Future research can build on these results to investigate the transition from ergodicity to many-body localization within photon gases, and to study how dimensionality and boundary conditions dictate the macroscopic thermodynamic properties of a quantum system. In conclusion, the findings described in this thesis contribute to a broader scientific effort to understand and control light as a state of matter. By investigating the fundamental mechanisms of tunneling and thermalization, this work provides the physical insights necessary to move beyond the constraints of current electronic architectures. While the development of large-scale photonic simulators remains a long-term objective, the methodologies and theoretical frameworks established here offer a cohesive narrative on how the structural control of light can lead to the observation and utilization of complex quantum phenomena.
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