By developing a `two-crystal method for color erasure, we can broaden the scope of chromatic interferometry to include optical photons whose frequency difference falls outside of the 400 nm to 4500 nm wavelength range, which is the passband of a PPLN
crystal. We demonstrate this possibility experimentally, by observing interference patterns between sources at 1064.4 nm and 1063.6 nm, corresponding to a frequency difference of about 200 GHz.
The Kuperberg invariant is a topological invariant of closed 3-manifolds based on finite-dimensional Hopf algebras. In this paper, we initiate the program of constructing 4-manifold invariants in the spirit of Kuperbergs 3-manifold invariant. We util
ize a structure called a Hopf triplet, which consists of three Hopf algebras and a bilinear form on each pair subject to certain compatibility conditions. In our construction, we present 4-manifolds by their trisection diagrams, a four-dimensional analog of Heegaard diagrams. The main result is that every Hopf triplet yields a diffeomorphism invariant of closed 4-manifolds. In special cases, our invariant reduces to Crane-Yetter invariants and generalized dichromatic invariants, and conjecturally Kashaevs invariant. As a starting point, we assume that the Hopf algebras involved in the Hopf triplets are semisimple. We speculate that relaxing semisimplicity will lead to even richer invariants.
We propose a quantum information based scheme to reduce the temperature of quantum many-body systems, and access regimes beyond the current capability of conventional cooling techniques. We show that collective measurements on multiple copies of a sy
stem at finite temperature can simulate measurements of the same system at a lower temperature. This idea is illustrated for the example of ultracold atoms in optical lattices, where controlled tunnel coupling and quantum gas microscopy can be naturally combined to realize the required collective measurements to access a lower, virtual temperature. Our protocol is experimentally implemented for a Bose-Hubbard model on up to 12 sites, and we successfully extract expectation values of observables at half the temperature of the physical system. Additionally, we present related techniques that enable the extraction of zero-temperature states directly.
We introduce a framework to study the emergence of time and causal structure in quantum many-body systems. In doing so, we consider quantum states which encode spacetime dynamics, and develop information theoretic tools to extract the causal relation
ships between putative spacetime subsystems. Our analysis reveals a quantum generalization of the thermodynamic arrow of time and begins to explore the roles of entanglement, scrambling and quantum error correction in the emergence of spacetime. For instance, exotic causal relationships can arise due to dynamically induced quantum error correction in spacetime: there can exist a spatial region in the past which does not causally influence any small spatial regions in the future, but yet it causally influences the union of several small spatial regions in the future. We provide examples of quantum causal influence in Hamiltonian evolution, quantum error correction codes, quantum teleportation, holographic tensor networks, the final state projection model of black holes, and many other systems. We find that the quantum causal influence provides a unifying perspective on spacetime correlations in these seemingly distinct settings. In addition, we prove a variety of general structural results and discuss the relation of quantum causal influence to spacetime quantum entropies.
We propose and demonstrate experimentally a scheme to create entangled history states of the Greenberger-Horne-Zeilinger (GHZ) type. In our experiment, the polarization states of a single photon at three different times are prepared as a GHZ entangle
d history state. We define a GHZ functional which attains a maximum value $1$ on the ideal GHZ entangled history state and is bounded above by $1/16$ for any three-time history state lacking tripartite entanglement. We have measured the GHZ functional on a state we have prepared experimentally, yielding a value of $0.656pm 0.005$, clearly demonstrating the contribution of entangled histories.
