Creation, manipulation and detection of anyons in optical lattices

2020

We study the dynamics of bosonic and fermionic anyons defined on a one-dimensional lattice, under the effect of Hamiltonians quadratic in creation and annihilation operators, commonly referred to as linear optics. These anyonic models are obtained from deformations of the standard bosonic or fermionic commutation relations via the introduction of a non-trivial exchange phase between different lattice sites. We study the effects of the anyonic exchange phase on the usual bosonic and fermionic bunching behaviors. We show how to exploit the inherent Aharonov-Bohm effect exhibited by these particles to build a deterministic, entangling two-qubit gate and prove quantum computational universality in these systems. We define coherent states for bosonic anyons and study their behavior under two-mode linear-optical devices. In particular we prove that, for a particular value of the exchange factor, an anyonic mirror can generate cat states, an important resource in quantum information proces...

Proceedings of the National Academy of Sciences, 2007

We study an implementation of a two-qubit universal quantum gate with neutral 87 Rb atoms trapped in a far-detuned two-color optical lattice. The qubit states j0i and j1i represent the ground and rst excited motional states of an atom in a laser induced potential well. By varying the ratio of the laser intensities of the two colors, the barrier between two neighboring atoms is lowered, creating two-particle entanglement. We predict the duration of operation of a conditional -phase gate with a time-dependent con guration interaction model.

Nature Physics, 2008

Strongly correlated quantum systems can exhibit exotic behaviour called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasiparticles with anyonic statistics and have been proposed as candidates for naturally error-free quantum computation. However, anyons have never been observed in nature directly. Here, we describe how to unambiguously detect and characterize such states in recently proposed spinlattice realizations using ultracold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by carrying out global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations.

Physical review letters, 2009

Contemporary Physics, 2004

We review novel methods to investigate, control and manipulate neutral atoms in optical lattices. These setups allow unprecedented quantum control over large numbers of atoms and thus are very promising for applications in quantum information processing. After introducing optical lattices we discuss the superfluid (SF) and Mott insulating (MI) states of neutral atoms trapped in such lattices and investigate the SF-MI transition as recently observed experimentally. In the second part of the paper we give an overview of proposals for quantum information processing and show different ways to entangle the trapped atoms, in particular the usage of cold collisions and Rydberg atoms. Finally, we also briefly discuss the implementation of quantum simulators, entanglement enhanced atom interferometers, and ideas for robust quantum memory in optical lattices.

Physical Review Letters, 2008

The mapping of photonic states to collective excitations of atomic ensembles is a powerful tool which finds a useful application in the realization of quantum memories and quantum repeaters. In this work we show that cold atoms in optical lattices can be used to perform an entangling unitary operation on the transferred atomic excitations. After the release of the quantum atomic state, our protocol results in a deterministic two qubit gate for photons. The proposed scheme is feasible with current experimental techniques and robust against the dominant sources of noise.

Physical Review Letters, 1999

We propose a new system for implementing quantum logic gates: neutral atoms trapped in a very far-off-resonance optical lattice. Pairs of atoms are made to occupy the same well by varying the polarization of the trapping lasers, and then a near-resonant electric dipole is induced by an auxiliary laser. A controlled-NOT can be implemented by conditioning the target atomic resonance on a resolvable level shift induced by the control atom. Atoms interact only during logical operations, thereby suppressing decoherence.

2011

Quantum computation provides a unique opportunity to explore new regimes of physical systems through the creation of non-trivial quantum states far outside of the classical limit. However, such computation is remarkably sensitive to noise and undergoes rapid dephasing in most cases. One potential solution to these prosaic concerns is to encode and process the information using topological manipulations of so-called anyons, particles in two dimensions with non-Abelian statistics. Unfortunately, practical implementation of such a topological system remains far from complete, both in terms of physical methods but also in terms of connecting the underlying topological field theory with a specific physical model, including the imperfections expected in any realistic device. Here we develop a complete picture of such topological quantum computation using a variation of the Kitaev honeycomb Hamiltonian as the basis for our approach. We show the robustness of this system against noise, confirm the non-Abelian statistics of the quasi-particles to be Ising anyons, and develop new techniques for turning topological information into measurable spin quantities.

Physical Review A, 2012

We describe how continuous-variable abelian anyons, created on the surface of a continuousvariable analogue of Kitaev's lattice model can be utilized for quantum computation. In particular, we derive protocols for the implementation of quantum gates using topological operations. We find that the topological operations alone are insufficient for universal quantum computation which leads us to study additional non-topological operations such as offline squeezing and single-mode measurements. It is shown that these in conjunction with a non-Gaussian element allow for universal quantum computation using continuous-variable abelian anyons.

Physical Review A, 1998

We study the means to prepare and coherently manipulate atomic wave packets in optical lattices, with particular emphasis on alkali atoms in the far-detuned limit. We derive a general, basis independent expression for the lattice operator, and show that its off-diagonal elements can be tailored to couple the vibrational manifolds of separate magnetic sublevels. Using these couplings one can evolve the state of a trapped atom in a quantum coherent fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We explore the use of atoms bound in optical lattices to study quantum tunneling and the generation of macroscopic superposition states in a double-well potential. Far-off-resonance optical potentials lend themselves particularly well to reservoir engineering via well controlled fluctuations in the potential, making the atom/lattice system attractive for the study of decoherence and the connection between classical and quantum physics.

Topological quantum computation using abelian anyons in Kitaev model is studied. We initially discuss the basics of quantum computation and then present a brief description of topological quantum computation using anyons. The exact solution of the 2D Kitaev model and the emergence of abelian anyons is also described. We also discuss quantum error correction and error tolerant quantum memory using Kitaev’s toric code. Abelian anyonic quantum computation, though not completely fault-tolerant, the universal gates can be realized by including some non topological operations with the topological operations. We verify an already proposed model to realize the universal gates in 2D Kitaev lattice by explicitly investigating the theoretical implementation. We find that the adiabatic transport of anyons for braiding cannot be directly represented by some loop operator if they are to be used for a controlled gate operation.

Scientific Reports, 2021

In this work, trapped ultracold atoms are proposed as a platform for efficient quantum gate circuits and algorithms. We also develop and evaluate quantum algorithms, including those for the Simon problem and the black-box string-finding problem. Our analytical model describes an open system with non-Hermitian Hamiltonian. It is shown that our proposed scheme offers better performance (in terms of the number of required gates and the processing time) for realizing the quantum gates and algorithms compared to previously reported approaches.

Physical Review A, 2005

The user has requested enhancement of the downloaded file. arXiv:cond-mat/0506316v2 [cond-mat.mes-hall] Abstract Based on the standard many-fermion field theory, we construct models describing ultracold fermions in a 1D optical lattice by implementing a mode expansion of the fermionic field operator where modes, in addition to space localisation, take into account the quantum numbers inherent in local fermion interactions. The resulting models are generalised Hubbard Hamiltonians whose interaction parameters are derived by a fully-analytical calculation. The special interest for this derivation resides in its model-generating capability and in the flexibility of the trapping techniques that allow the tuning of the Hamiltonian interaction parameters over a wide range of values. While the Hubbard Hamiltonian is recovered in a very low-density regime, in general, far more complicated Hamiltonians characterise high-density regimes, revealing a rich scenario for both the phenomenology of interacting trapped fermions and the experimental realization of devices for quantum information processing. As a first example of the different situations that may arise beyond the models well known in the literature (the unpolarised-spin fermion model and the noninteracting spin-polarised fermion model), we derive a Rotational Hubbard Hamiltonian describing the local rotational activity of spin-polarised fermions. Based on a standard techniques we obtain the mean-field version of our model Hamiltonian and show how different dynamical algebras characterize the case of attractive and repulsive two-body potentials.

Physical Review Letters, 2005

We describe a method to create fractional quantum Hall states of atoms confined in optical lattices. We show that the dynamics of the atoms in the lattice is analogous to the motion of a charged particle in a magnetic field if an oscillating quadrupole potential is applied together with a periodic modulation of the tunneling between lattice sites. We demonstrate that in a suitable parameter regime the ground state in the lattice is of the fractional quantum Hall type and we show how these states can be reached by melting a Mott insulator state in a super lattice potential. Finally we discuss techniques to observe these strongly correlated states. PACS numbers: 03.75.Lm, Ultra-cold atomic gasses [1] provide a unique access to quantum many body systems with well understood and controllable interactions. Whereas most of the experiments in this field have been carried out in the regime of weak interactions, the recent achievements involving Feshbach resonances [2] and the realization of a Mottinsulator state of atoms in optical lattices enters into the regime of strong interaction with a richer and more complex many body dynamics. At the same time a realization of strongly correlated states of fractional quantum Hall type [5] has recently been suggested in cold atomic gases . These proposals involve atoms in rotating harmonic traps, which mimic the effective magnetic field. However, weak interaction between the particles (and correspondingly small gap in the excitation spectrum), required precision on trap rotation and finite temperature effects make these proposals difficult to realize experimentally. In this Letter we present a novel method that uses atoms in optical lattices to create states of the fractional quantum Hall type. Since the interactions of atoms localized in the lattices are strongly enhanced compared to the interaction of atoms in free space, these states are characterized by large energy gaps.