To gain deeper insight into the dynamics of complex quantum systems we need a quantum leap in computer simulations. We can not translate quantum behaviour arising with superposition states or entanglement efficiently into the classical language of conventional computers. The final solution to this problem is a universal quantum computer [1], suggested in 1982 and envisioned to become functional within the next decade(s); a shortcut was proposed via simulating the quantum behaviour of interest in a different quantum system, where all parameters and interactions can be controlled and the outcome detected sufficiently well.Here we study the feasibility of a quantum simulator based on trapped ions [2]. We experimentally simulate the adiabatic evolution of the smallest non-trivial spin system from the paramagnetic into the (anti-)ferromagnetic order with a quantum magnetisation for two spins of 98%, controlling and manipulating all relevant parameters of the Hamiltonian independently via electromagnetic fields. We prove that the observed transition is not driven by thermal fluctuations, but of quantum mechanical origin, the source of quantum fluctuations in quantum phase transitions [3]. We observe a final superposition state of the two degenerate spin configurations for the ferromagnetic (|↑↑ +|↓↓ ) and the anti-ferromagnetic (|↑↓ + |↓↑ ) order, respectively. These correspond to deterministically entangled states achieved with a fidelity up to 88%.Our work demonstrates a building block for simulating quantum spin-Hamiltonians with trapped ions. The method has potential for scaling to a higher number of coupled spins [2].
We implement the proof of principle for the quantum walk of one ion in a linear ion trap. With a single-step fidelity exceeding 0.99, we perform three steps of an asymmetric walk on the line. We clearly reveal the differences to its classical counterpart if we allow the walker/ion to take all classical paths simultaneously. Quantum interferences enforce asymmetric, non-classical distributions in the highly entangled degrees of freedom (of coin and position states). We theoretically study and experimentally observe the limitation in the number of steps of our approach, that is imposed by motional squeezing. We propose an altered protocol based on methods of impulsive steps to overcome these restrictions, in principal allowing to scale the quantum walk to several hundreds of steps.PACS numbers: 03.67. Ac, 05.40Fb, 0504Jc A quantum walk[1] is the deterministic quantum mechanical extension of a classical random walk. A simple classical version requires two basic operations: Tossing the coin (coin-operation), allowing for two possible and random outcomes. Dependent on this outcome, the walker performs a step to the right or left (stepoperation). In the quantum mechanical extension the operations allow for coherent superpositions of entangled coin and position states. After several iterations the probability to be in a certain position is determined by quantum mechanical interference of the walker state that leads to fundamentally different characteristics of the walk [2].The motivation for studying quantum walks is twofold. On the one hand, many classical algorithms include random walks. Examples can be found in biology, psychology, economics and physics, for example Einstein's simple model for Brownian motion [3]. The extension of the walk to quantum mechanics might allow for substantial speedup of related quantum versions [2], as in prominent algorithms suggested by Shor[4] and Grover [5] due to other quantum-subroutines. On the other hand, the quantum walk could lead to new insights into entanglement and decoherence in mesoscopic systems [6]. These topics might be explored by increasing the amount of walkers -even before any algorithm might benefit from the quantum random walk.Quantum walks have been thoroughly investigated theoretically and first attempts at implementation have been performed with a very limited amount of steps due to a lack of operation fidelity or fundamental restrictions within the protocol. Some aspects have been realized on the longitudinal modes of a linear optical resonator [7] and in a nuclear magnetic resonance experiment [8]. An implementation based on neutral atoms in a spin-dependent optical lattice[9, 10, 11] has resulted in an experiment recently. Other proposals considered an array of microtraps illuminated by a set of microlenses [12] and Bose-Einstein condensates [13]. Travaglione and Milburn[14] proposed a scheme for trapped ions to transfer the high operational fidelities [6] obtained in quantum information processing (QIP) into To implement the deterministic "tossing of t...
We study phonons in a dynamical chain of ions confined by a trap with a time-dependent (axial) potential strength and demonstrate that they behave in the same way as quantum fields in an expanding or contracting Universe. Based on this analogy, we present a scheme for the detection of the analogue of cosmological particle creation which should be feasible with present day technology. In order to test the quantum nature of the particle creation mechanism and to distinguish it from classical effects such as heating, we propose to measure the two-phonon amplitude via the 2nd red sideband transition and to compare it with the one-phonon amplitude (1st red sideband).
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