arXiv subjects

Anne E. B. Nielsen

Publications and source records attributed to Anne E. B. Nielsen.

At least 73 records · Page 4Linked to original sources

arXiv2015

Bosonic fractional quantum Hall states on the torus from conformal field theory

The Kalmeyer-Laughlin state, which is a lattice version of the bosonic Laughlin state at filling factor one half, has attracted much attention due to its topological and chiral spin liquid properties. Here we show that the Kalmeyer-Laughlin state on the torus can be expressed in terms of a correlator of conformal fields from the $SU(2)_1$ Wess-Zumino-Witten model. This reveals an interesting underlying mathematical structure and provides a natural way to generalize the Kalmeyer-Laughlin state to arbitrary lattices on the torus. We find that the many-body Chern number of the states is unity for more different lattices, which suggests that the topological properties of the states are preserved when the lattice is changed. Finally, we analyze the symmetry properties of the states on square lattices.

cond-mat.str-el↗

arXiv2014

Anyon braiding in semi-analytical fractional quantum Hall lattice models

It has been demonstrated numerically, mainly by considering ground state properties, that fractional quantum Hall physics can appear in lattice systems, but it is very difficult to study the anyons directly. Here, I propose to solve this problem by using conformal field theory to build semi-analytical fractional quantum Hall lattice models having anyons in their ground states, and I carry out the construction explicitly for the family of bosonic and fermionic Laughlin states. This enables me to show directly that the braiding properties of the anyons are those expected from analytical continuation of the wave functions and to compute properties such as internal structure, size, and charge of the anyons with simple Monte Carlo simulations. The models can also be used to study how the anyons behave when they approach or even pass through the edge of the sample. Finally, I compute the effective magnetic field seen by the anyons, which varies periodically due to the presence of the lattice.

cond-mat.str-el↗

arXiv2014

An efficient all-optical switch using a lambda atom in a cavity QED system

We propose an all-optical switch constructed from a two-mode optical resonator containing a strongly coupled, three-state system. The coupling allows a weak, continuous wave laser drive to incoherently control the transmission of a much stronger, continuous wave signal laser into (and through) the resonator. We demonstrate that in this simple setup the presence of a control drive with one tenth the power of the signal drive can induce near complete reflection of the signal, while its absence allows for near complete transmission. The switch can also be operated as a set-reset relay with two control inputs that efficiently drive the switch into either the reflecting or the transmitting state.

quant-ph↗

arXiv2014

Single photon state generation from a continuous-wave non-degenerate optical parametric oscillator

We present a theoretical treatment of conditional preparation of one-photon states from a continuous-wave non-degenerate optical parametric oscillator. We obtain an analytical expression for the output state Wigner function, and we maximize the one-photon state fidelity by varying the temporal mode function of the output state. We show that a higher production rate of high fidelity Fock states is obtained if we condition the outcome on dark intervals around trigger photo detection events.

quant-ph↗

arXiv2014

Transforming squeezed light into a large amplitude coherent state superposition

A quantum superposition of two coherent states of light with small amplitude can be obtained by subtracting a photon from a squeezed vacuum state. In experiments this preparation can be made conditioned on the detection of a photon in the field from a squeezed light source. We propose and analyze an extended measurement strategy which allows generation of high fidelity coherent state superpositions with larger amplitude.

quant-ph↗

arXiv2014

Fighting decoherence in a continuous two-qubit odd or even parity measurement with a closed-loop setup

A parity measurement on two qubits, each consisting of a single atom in a cavity, can be realized by measuring the phase shift of a probe beam, which interacts sequentially with the two qubits, but imperfections lead to decoherence within the subspaces of a given parity. We demonstrate that a different setup, where the probe light interacts repeatedly with the qubits, can reduce the rate of decoherence within the odd or the even parity subspace significantly. We consider both the case of a resonant and the case of a nonresonant light-atom interaction and find that the performance is comparable if the parameters are chosen appropriately.

quant-ph↗

arXiv2014

Construction of spin models displaying quantum criticality from quantum field theory

We provide a method for constructing finite temperature states of one-dimensional spin chains displaying quantum criticality. These models are constructed using correlators of products of quantum fields and have an analytical purification. Their properties can be investigated by Monte-Carlo simulations, which enable us to study the low-temperature phase diagram and to show that it displays a region of quantum criticality. The mixed states obtained are shown to be close to the thermal state of a simple nearest neighbour Hamiltonian.

cond-mat.str-el↗

arXiv2014

Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model

We propose 1D and 2D lattice wave functions constructed from the SU(n)_1 Wess-Zumino-Witten (WZW) model and derive their parent Hamiltonians. When all spins in the lattice transform under SU(n) fundamental representations, we obtain a two-body Hamiltonian in 1D, including the SU(n) Haldane-Shastry model as a special case. In 2D, we show that the wave function converges to a class of Halperin's multilayer fractional quantum Hall states and belongs to chiral spin liquids. Our result reveals a hidden SU(n) symmetry for this class of Halperin states. When the spins sit on bipartite lattices with alternating fundamental and conjugate representations, we provide numerical evidence that the state in 1D exhibits quantum criticality deviating from the expected behaviors of the SU(n)_1 WZW model, while in 2D they are chiral spin liquids being consistent with the prediction of the SU(n)_1 WZW model.

cond-mat.str-el↗

arXiv2014

Optical lattice implementation scheme of a bosonic topological model with fermionic atoms

We present a scheme to implement a Fermi-Hubbard-like model in ultracold atoms in optical lattices and analyze the topological features of its ground state. In particular, we show that the ground state for appropriate parameters has a large overlap with a lattice version of the bosonic Laughlin state at filling factor one half. The scheme utilizes laser assisted and normal tunnelling in a checkerboard optical lattice. The requirements on temperature, interactions, and hopping strengths are similar to those needed to observe the Néel antiferromagnetic ordering in the standard Fermi-Hubbard model in the Mott insulating regime.

cond-mat.str-el↗

arXiv2013

Lattice Laughlin States of Bosons and Fermions at Filling Fractions $1/q$

We introduce a two-parameter family of strongly-correlated wave functions for bosons and fermions in lattices. One parameter, $q$, is connected to the filling fraction. The other one, $η$, allows us to interpolate between the lattice limit ($η=1$) and the continuum limit ($η\to 0^+$) of families of states appearing in the context of the fractional quantum Hall effect or the Calogero-Sutherland model. We give evidence that the main physical properties along the interpolation remain the same. Finally, in the lattice limit, we derive parent Hamiltonians for those wave functions and in 1D, we determine part of the low energy spectrum.

cond-mat.str-el↗

arXiv2013

Fractional quantum Hall states in lattices: Local models and physical implementation

The fractional quantum Hall (FQH) effect is one of the most striking phenomena in condensed matter physics. It is described by a simple Laughlin wavefunction and has been thoroughly studied both theoretically and experimentally. In lattice systems, however, such an effect has not been observed, there are few simple models displaying it, and only few mechanisms leading to it are known. Here we propose a new way of constructing lattice Hamiltonians with local interactions and FQH like ground states. In particular, we obtain a spin 1/2 model with a bosonic Laughlin like ground state, displaying a variety of topological features. We also demonstrate how such a model naturally emerges out of a Fermi-Hubbard like model at half filling, in which the kinetic energy part possesses bands with nonzero Chern number, and we show how this model can be implemented in an optical lattice setup with present technology.

cond-mat.str-el↗

arXiv2012

Laughlin spin liquid states on lattices obtained from conformal field theory

We propose a set of spin system wavefunctions that are very similar to lattice versions of the Laughlin states. The wavefunction are conformal blocks of conformal field theories, and for filling factor ν=1/2 we provide a parent Hamiltonian, which is valid for any even number of spins and is at the same time a 2D generalization of the Haldane-Shastry model. We also demonstrate that the Kalmeyer-Laughlin state is reproduced as a particular case of this model. Finally, we discuss various properties of the spin states and point out several analogies to known results for the Laughlin states.

cond-mat.str-el↗

arXiv2011

Quantum spin Hamiltonians for the SU(2)_k WZW model

We propose to use null vectors in conformal field theories to derive model Hamiltonians of quantum spin chains and corresponding ground state wave function(s). The approach is quite general, and we illustrate it by constructing a family of Hamiltonians whose ground states are the chiral correlators of the SU(2)_k WZW model for integer values of the level k. The simplest example corresponds to k=1 and is essentially a nonuniform generalization of the Haldane-Shastry model with long-range exchange couplings. At level k=2, we analyze the model for N spin 1 fields. We find that the Renyi entropy and the two-point spin correlator show, respectively, logarithmic growth and algebraic decay. Furthermore, we use the null vectors to derive a set of algebraic, linear equations relating spin correlators within each model. At level k=1, these equations allow us to compute the two-point spin correlators analytically for the finite chain uniform Haldane-Shastry model and to obtain numerical results for the nonuniform case and for higher-point spin correlators in a very simple way and without resorting to Monte Carlo techniques.

cond-mat.str-el↗

arXiv2011

Violation of the area law and long range correlations in infinite matrix product states

We propose to construct a family of states of one-dimensional spin chains by replacing the finite dimensional matrices in matrix product states by infinite dimensional operators constructed from bosonic annihilation and creation operators. The resulting states are demonstrated to violate the area law and to exhibit long range correlations. In addition, we propose an efficient way to prepare the states experimentally, in which the spins interact sequentially with an ancilla system.

cond-mat.str-el↗

arXiv2010

Topological matter with collective encoding and Rydberg blockade

We propose to use a permutation symmetric sample of multi-level atoms to simulate the properties of topologically ordered states. The Rydberg blockade interaction is used to prepare states of the sample which are equivalent to resonating valence bond states, Laughlin states, and string-net condensates and to create and study the properties of their quasi-particle-like fundamental excitations.

quant-ph↗

arXiv2010

Quantum state engineering, purification, and number resolved photon detection with high finesse optical cavities

We propose and analyze a multi-functional setup consisting of high finesse optical cavities, beam splitters, and phase shifters. The basic scheme projects arbitrary photonic two-mode input states onto the subspace spanned by the product of Fock states |n>|n> with n=0,1,2,.... This protocol does not only provide the possibility to conditionally generate highly entangled photon number states as resource for quantum information protocols but also allows one to test and hence purify this type of quantum states in a communication scenario, which is of great practical importance. The scheme is especially attractive as a generalization to many modes allows for distribution and purification of entanglement in networks. In an alternative working mode, the setup allows of quantum non demolition number resolved photodetection in the optical domain.

quant-ph↗

arXiv2010

Deterministic multi-mode photonic device for quantum information processing

We propose the implementation of a light source, which can deterministically generate a rich variety of multi-mode quantum states. The desired states are encoded in the collective population of different ground hyperfine states of an atomic ensemble and converted to multi-mode photonic states by excitation to optically excited levels followed by cooperative spontaneous emission. Among our examples of applications, we demonstrate how two-photon entangled states can be prepared and implemented in a protocol for reference frame free quantum key distribution and how one-dimensional as well as higher-dimensional cluster states can be produced.

quant-ph↗

arXiv2009

Quantum filter reduction for measurement-feedback control via unsupervised manifold learning

We derive simple models for the dynamics of a single atom coupled to a cavity field mode in the absorptive bistable parameter regime by projecting the time evolution of the state of the system onto a suitably chosen nonlinear low-dimensional manifold, which is found by use of local tangent space alignment. The output field from the cavity is detected with a homodyne detector allowing observation of quantum jumps of the system between states with different average numbers of photons in the cavity. We find that the models, which are significantly faster to integrate numerically than the full stochastic master equation, largely reproduce the dynamics of the system, and we demonstrate that they are sufficiently accurate to facilitate feedback control of the state of the system based on the predictions of the models alone.

quant-ph↗