Holographic realization of the prime number quantum potential.

We report the experimental realization of the prime number quantum potential VN (x), defined as the potential entering the single-particle Schrödinger Hamiltonian with eigenvalues given by the first N prime numbers. Using computer-generated holography, we create light intensity profiles suitable to optically trap ultracold atoms in these potentials for different N values. As a further application, we also implement a potential whose spectrum is given by the lucky numbers, a sequence of integers generated by a different sieve than the familiar Eratosthenes's sieve used for the primes. Our results pave the way toward the realization of quantum potentials with arbitrary sequences of integers as energy levels and show, in perspective, the possibility to set up quantum systems for arithmetic manipulations or mathematical tests involving prime numbers.

E_{8} Spectra of Quasi-One-Dimensional Antiferromagnet BaCo_{2}V_{2}O_{8} under Transverse Field.

We report ^{51}V NMR and inelastic neutron scattering (INS) measurements on a quasi-1D antiferromagnet BaCo_{2}V_{2}O_{8} under transverse field along the [010] direction. The scaling behavior of the spin-lattice relaxation rate above the Néel temperatures unveils a 1D quantum critical point (QCP) at H_{c}^{1D}≈4.7 T, which is masked by the 3D magnetic order. With the aid of accurate analytical analysis and numerical calculations, we show that the zone center INS spectrum at H_{c}^{1D} is precisely described by the pattern of the 1D quantum Ising model in a magnetic field, a class of universality described in terms of the exceptional E_{8} Lie algebra. These excitations are nondiffusive over a certain field range when the system is away from the 1D QCP. Our results provide an unambiguous experimental realization of the massive E_{8} phase in the compound, and open a new experimental route for exploring the dynamics of quantum integrable systems as well as physics beyond integrability.

Prime Suspects in a Quantum Ladder.

In this Letter we set up a suggestive number theory interpretation of a quantum ladder system made of N coupled chains of spin 1/2. Using the hard-core boson representation and a leg-Hamiltonian made of a magnetic field and a hopping term, we can associate to the spins σ_{a} the prime numbers p_{a} so that the chains become quantum registers for square-free integers. The rung Hamiltonian involves permutation terms between next-neighbor chains and a coprime repulsive interaction. The system has various phases; in particular, there is one whose ground state is a coherent superposition of the first N prime numbers. We also discuss the realization of such a model in terms of an open quantum system with a dissipative Lindblad dynamics.

Topological quantum hashing with the icosahedral group.

We study an efficient algorithm to hash any single-qubit gate into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudogroups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O(log2(1/epsilon)), we can approximate all SU(2) matrices to an average error epsilon with a cost of O(log(1/epsilon)) in time. The algorithm is applicable to generic quantum compiling.

Effective thermal dynamics following a quantum quench in a spin chain.

We study the nonequilibrium dynamics of the quantum Ising model following an abrupt quench of the transverse field. We focus on the on-site autocorrelation function of the order parameter, and extract the phase-coherence time tau(Q)(phi) from its asymptotic behavior. We show that the initial state determines tau(Q)(phi) only through an effective temperature set by its energy and the final Hamiltonian. Moreover, we observe that the dependence of tau(Q)(phi) on the effective temperature fairly agrees with that obtained in thermal equilibrium as a function of the equilibrium temperature.