Showing papers on "Coherent states published in 2015"

Confining the state of light to a quantum manifold by engineered two-photon loss

Abstract: Physical systems usually exhibit quantum behavior, such as superpositions and entanglement, only when they are sufficiently decoupled from a lossy environment. Paradoxically, a specially engineered interaction with the environment can become a resource for the generation and protection of quantum states. This notion can be generalized to the confinement of a system into a manifold of quantum states, consisting of all coherent superpositions of multiple stable steady states. We have confined the state of a superconducting resonator to the quantum manifold spanned by two coherent states of opposite phases and have observed a Schrodinger cat state spontaneously squeeze out of vacuum before decaying into a classical mixture. This experiment points toward robustly encoding quantum information in multidimensional steady-state manifolds.

Composable security proof for continuous-variable quantum key distribution with coherent States.

Abstract: We give the first composable security proof for continuous-variable quantum key distribution with coherent states against collective attacks. Crucially, in the limit of large blocks the secret key rate converges to the usual value computed from the Holevo bound. Combining our proof with either the de Finetti theorem or the postselection technique then shows the security of the protocol against general attacks, thereby confirming the long-standing conjecture that Gaussian attacks are optimal asymptotically in the composable security framework. We expect that our parameter estimation procedure, which does not rely on any assumption about the quantum state being measured, will find applications elsewhere, for instance, for the reliable quantification of continuous-variable entanglement in finite-size settings.

Quantum harmonic oscillator state synthesis by reservoir engineering

Abstract: The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to generate squeezed, coherent, and displaced-squeezed states as steady states in the presence of noise. We verify the created state by generating two-state correlated spin-motion Rabi oscillations, resulting in high-contrast measurements. For both cooling and measurement, we use spin-oscillator couplings that provide transitions between oscillator states in an engineered Fock state basis. Our approach should facilitate studies of entanglement, quantum computation, and open-system quantum simulations in a wide range of physical systems.

Quantitative Derivation of the Gross-Pitaevskii Equation

Abstract: Starting from first-principle many-body quantum dynamics, we show that the dynamics of Bose-Einstein condensates can be approximated by the time-dependent nonlinear Gross-Pitaevskii equation, giving a bound on the rate of the convergence. Initial data are constructed on the bosonic Fock space applying an appropriate Bogoliubov transformation on a coherent state with expected number of particles $\mathit{N}$. The Bogoliubov transformation plays a crucial role; it produces the correct microscopic correlations among the particles. Our analysis shows that, on the level of the one-particle reduced density, the form of the initial data is preserved by the many-body evolution, up to a small error that vanishes as $\mathit{N}^{-1/2}$ in the limit of large $\mathit{N}$.

Noise-induced effects in nonlinear relaxation of condensed matter systems

Abstract: Noise-induced phenomena characterise the nonlinear relaxation of nonequilibrium physical systems towards equilibrium states. Often, this relaxation process proceeds through metastable states and the noise can give rise to resonant phenomena with an enhancement of lifetime of these states or some coherent state of the condensed matter system considered. In this paper three noise induced phenomena, namely the noise enhanced stability, the stochastic resonant activation and the noise-induced coherence of electron spin, are reviewed in the nonlinear relaxation dynamics of three different systems of condensed matter: (i) a long-overlap Josephson junction (JJ) subject to thermal fluctuations and non-Gaussian, Levy distributed, noise sources; (ii) a graphene-based Josephson junction subject to thermal fluctuations; (iii) electrons in a n-type GaAs crystal driven by a fluctuating electric field. In the first system, we focus on the switching events from the superconducting metastable state to the resistive state, by solving the perturbed stochastic sine-Gordon equation. Nonmonotonic behaviours of the mean switching time versus the noise intensity, frequency of the external driving, and length of the junction are obtained. Moreover, the influence of the noise induced solitons on the mean switching time behaviour is shown. In the second system, noise induced phenomena are observed, such as noise enhanced stability (NES) and stochastic resonant activation (SRA). In the third system, the spin polarised transport in GaAs is explored in two different scenarios, i.e. in the presence of Gaussian correlated fluctuations or symmetric dichotomous noise. Numerical results indicate an increase of the electron spin lifetime by rising the strength of the random fluctuating component. Furthermore, our findings for the electron spin depolarization time as a function of the noise correlation time point out (i) a non-monotonic behaviour with a maximum in the case of Gaussian correlated fluctuations, (ii) an increase up to a plateau in the case of dichotomous noise. The noise enhances the coherence of the spin relaxation process.

Joint estimation of phase and phase diffusion for quantum metrology

Abstract: Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here we investigate the joint estimation of a phase shift and the amplitude of phase diffusion at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshaped as a two-dimensional Hilbert space model, encompassing the description of an interferometer phase probed with relevant quantum states--split single-photons, coherent states or N00N states. For these cases, we obtain a trade-off bound on the statistical variances for the joint estimation of phase and phase diffusion, as well as optimum measurement schemes. We use this bound to quantify the effectiveness of an actual experimental set-up for joint parameter estimation for polarimetry. We conclude by discussing the form of the trade-off relations for more general states and measurements.

Generation of a squeezed state of an oscillator by stroboscopic back-action-evading measurement

Abstract: Squeezed states make it possible to circumvent the standard quantum limit. Using stroboscopic measurements one can create squeezed states of a rather unusual oscillator: the collective spin of an atomic ensemble precessing in a magnetic field. Continuous observation of an oscillator results in quantum back-action, which limits the knowledge acquired by the measurement. A careful balance between the information obtained and the back-action disturbance leads to the standard quantum limit of precision. This limit can be surpassed by a measurement with strength modulated at twice the oscillator frequency, resulting in a squeezed state of the oscillator motion, as proposed decades ago1,2,3. Here, we report the generation of a squeezed state of an oscillator by a stroboscopic back-action-evading measurement. The oscillator is the spin of an atomic ensemble precessing in a magnetic field. The oscillator initially prepared nearly in the ground state is stroboscopically coupled to an optical mode of a cavity. A measurement of the output light results in a 2.2 ± 0.3 dB squeezed state of the oscillator. The demonstrated spin-squeezed state of 108 atoms with an angular spin variance of 8 × 10−10 rad2 is promising for magnetic field sensing.

Resolving the vacuum fluctuations of an optomechanical system using an artificial atom

Abstract: Vacuum fluctuations in a ground-state mechanical oscillator are hard to distinguish from noise, but by using the coupling with a superconducting qubit in a microwave cavity one can amplify and convert them to directly measurable real photons. Heisenberg’s uncertainty principle results in one of the strangest quantum behaviours: a mechanical oscillator can never truly be at rest. Even at a temperature of absolute zero, its position and momentum are still subject to quantum fluctuations1,2. However, direct energy detection of the oscillator in its ground state makes it seem motionless1,3, and in linear position measurements detector noise can masquerade as mechanical fluctuations4,5,6,7. Thus, how can we resolve quantum fluctuations? Here, we parametrically couple a micromechanical oscillator to a microwave cavity to prepare the system in its quantum ground state8,9 and then amplify the remaining vacuum fluctuations into real energy quanta10. We monitor the photon/phonon-number distributions using a superconducting qubit11,12,13, allowing us to resolve the quantum vacuum fluctuations of the macroscopic oscillator’s motion. Our results further demonstrate the ability to control a long-lived mechanical oscillator using a non-Gaussian resource, directly enabling applications in quantum information processing and enhanced detection of displacement and forces.

Effective Evolution Equations from Quantum Dynamics

Abstract: These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrodinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems and their time evolution. Section 2 introduces the mean-field regime for bosonic systems and explains how the many-body dynamics can be approximated in this limit using the Hartree equation. Section 3 presents a method, based on the use of coherent states, for rigorously proving the convergence towards the Hartree dynamics, while the fluctuations around the Hartree equation are considered in Section 4. Section 5 focuses on a discussion of a more subtle regime, in which the many-body evolution can be approximated by means of the nonlinear Gross-Pitaevskii equation. Section 6 addresses fermionic systems (characterized by antisymmetric wave functions); here, the fermionic mean-field regime is naturally linked with a semiclassical regime, and it is proven that the evolution of approximate Slater determinants can be approximated using the nonlinear Hartree-Fock equation. In closing, Section 7 reexamines the same fermionic mean-field regime, but with a focus on mixed quasi-free initial data approximating thermal states at positive temperature.

Fluctuations around Hartree states in the mean-field regime

Abstract: We consider the dynamics of a large system of $N$ interacting bosons in the mean-field regime where the interaction is of order $1/N$. We prove that the fluctuations around the nonlinear Hartree state are generated by an effective quadratic Hamiltonian in Fock space, which is derived from Bogoliubov's approximation. We use a direct method in the $N$-particle space, which is different from the one based on coherent states in Fock space.

Spin–motion entanglement and state diagnosis with squeezed oscillator wavepackets

Abstract: Mesoscopic superpositions of distinguishable coherent states provide an analogue of the 'Schrodinger's cat' thought experiment. For mechanical oscillators these have primarily been realized using coherent wavepackets, for which the distinguishability arises as a result of the spatial separation of the superposed states. Here we demonstrate superpositions composed of squeezed wavepackets, which we generate by applying an internal-state-dependent force to a single trapped ion initialized in a squeezed vacuum state with nine decibel reduction in the quadrature variance. This allows us to characterize the initial squeezed wavepacket by monitoring the onset of spin-motion entanglement, and to verify the evolution of the number states of the oscillator as a function of the duration of the force. In both cases we observe clear differences between displacements aligned with the squeezed and anti-squeezed axes. We observe coherent revivals when inverting the state-dependent force after separating the wavepackets by more than 19 times the ground-state root mean squared extent, which corresponds to 56 times the root mean squared extent of the squeezed wavepacket along the displacement direction. Aside from their fundamental nature, these states may be useful for quantum metrology or quantum information processing with continuous variables.

Scan-free direct measurement of an extremely high-dimensional photonic state

Abstract: Retrieving the vast amount of information carried by a photon is an enduring challenge in quantum metrology science and quantum photonics research. The transverse spatial state of a photon is a convenient high-dimensional quantum system for study, as it has a well-understood classical analog as the transverse complex field profile of an optical beam. One severe drawback of all currently available quantum metrology techniques is the need for a time-consuming characterization process, which scales very unfavorably with the dimensionality of the quantum system. Here we demonstrate a technique that directly measures a million-dimensional photonic spatial state with a single setting of the measurement apparatus. Through the arrangement of a weak measurement of momentum and parallel strong measurements of position, the complex values of the entire photon state vector become measurable directly. The dimension of our measured state is approximately four orders of magnitude larger than previously measured. Our work opens up a practical route for characterizing high-dimensional quantum systems in real time. Furthermore, our demonstration also serves as a high-speed, extremely high-resolution unambiguous complex field measurement technique for diverse classical applications.

Statistical mixtures of states can be more quantum than their superpositions: Comparison of nonclassicality measures for single-qubit states

Abstract: A bosonic state is commonly considered nonclassical (or quantum) if its Glauber-Sudarshan $P$ function is not a classical probability density, which implies that only coherent states and their statistical mixtures are classical. We quantify the nonclassicality of a single qubit, defined by the vacuum and single-photon states, by applying the following four well-known measures of nonclassicality: (1) the nonclassical depth, $\ensuremath{\tau}$, related to the minimal amount of Gaussian noise which changes a nonpositive $P$ function into a positive one; (2) the nonclassical distance $D$, defined as the Bures distance of a given state to the closest classical state, which is the vacuum for the single-qubit Hilbert space; together with (3) the negativity potential (NP), and (4) concurrence potential, which are the nonclassicality measures corresponding to the entanglement measures (i.e., the negativity and concurrence, respectively) for the state generated by mixing a single-qubit state with the vacuum on a balanced beam splitter. We show that complete statistical mixtures of the vacuum and single-photon states are the most nonclassical single-qubit states regarding the distance $D$ for a fixed value of both the depth $\ensuremath{\tau}$ and NP in the whole range $[0,1]$ of their values, as well as the NP for a given value of $\ensuremath{\tau}$ such that $\ensuremath{\tau}g0.315\phantom{\rule{0.16em}{0ex}}4$. Conversely, pure states are the most nonclassical single-qubit states with respect to $\ensuremath{\tau}$ for a given $D$, NP versus $D$, and $\ensuremath{\tau}$ versus NP. We also show the ``relativity'' of these nonclassicality measures by comparing pairs of single-qubit states: if a state is less nonclassical than another state according to some measure then it might be more nonclassical according to another measure. Moreover, we find that the concurrence potential is equal to the nonclassical distance for single-qubit states. This implies an operational interpretation of the nonclassical distance as the potential for the entanglement of formation.

Coherence measures and optimal conversion for coherent states

Abstract: We discuss a general strategy to construct coherence measures. One can build an important class of coherence measures which cover the relative entropy measure for pure states, the l1-norm measure for pure states and the α-entropy measure. The optimal conversion of coherent states under incoherent operations is presented which sheds some light on the coherence of a single copy of a pure state.

Work extraction from heat-powered quantized optomechanical setups

Abstract: We analyze work extraction from an autonomous (self-contained) heat-powered optomechanical setup. The initial state of the quantized mechanical oscillator plays a key role. As the initial mean amplitude of the oscillator decreases, the resulting efficiency increases. In contrast to laser-powered self-induced oscillations, work extraction from a broadband heat bath does not require coherence or phase-locking: an initial phase-averaged coherent state of the oscillator still yields work, as opposed to an initial Fock-state.

Continuous-variable quantum teleportation with non-Gaussian entangled states generated via multiple-photon subtraction and addition

Abstract: We theoretically analyze the Einstein-Podolsky-Rosen (EPR) correlation, the quadrature squeezing, and the continuous-variable quantum teleportation when considering non-Gaussian entangled states generated by applying multiple-photon subtraction and multiple-photon addition to a two-mode squeezed vacuum state (TMSVs). Our results indicate that in the case of the multiple-photon-subtracted TMSVs with symmetric operations, the corresponding EPR correlation, the two-mode squeezing degree, the sum squeezing, and the fidelity of teleporting a coherent state or a squeezed vacuum state can be enhanced for any squeezing parameter $r$ and these enhancements increase with the number of subtracted photons in the low-squeezing regime, while asymmetric multiple-photon subtractions will generally reduce these quantities. For the multiple-photon-added TMSVs, although it holds stronger entanglement, its EPR correlation, two-mode squeezing, sum squeezing, and the fidelity of a coherent state are always smaller than that of the TMSVs. Only when considering the case of teleporting a squeezed vacuum state does the symmetric photon addition make somewhat of an improvement in the fidelity for large-squeezing parameters. In addition, we analytically prove that a one-mode multiple-photon-subtracted TMSVs is equivalent to that of the one-mode multiple-photon-added one. And one-mode multiple-photon operations will diminish the above four quantities for any squeezing parameter $r$.

Coherent control of plasma dynamics

Abstract: Coherent control of a system involves steering an interaction to a final coherent state by controlling the phase of an applied field. Plasmas support coherent wave structures that can be generated by intense laser fields. Here, we demonstrate the coherent control of plasma dynamics in a laser wakefield electron acceleration experiment. A genetic algorithm is implemented using a deformable mirror with the electron beam signal as feedback, which allows a heuristic search for the optimal wavefront under laser-plasma conditions that is not known a priori. We are able to improve both the electron beam charge and angular distribution by an order of magnitude. These improvements do not simply correlate with having the 'best' focal spot, as the highest quality vacuum focal spot produces a greatly inferior electron beam, but instead correspond to the particular laser phase front that steers the plasma wave to a final state with optimal accelerating fields.

Discrete-phase-randomized coherent state source and its application in quantum key distribution

Abstract: Coherent state photon sources are widely used in quantum information processing. In many applications, such as quantum key distribution (QKD), a coherent state functions as a mixture of Fock states by assuming that its phase is continuously randomized. In practice, such a crucial assumption is often not satisfied, and therefore the security of existing QKD experiments is not guaranteed. To bridge this gap, we provide a rigorous security proof of QKD with discrete-phase-randomized coherent state sources. Our results show that the performance of the discrete-phase randomization case is close to its continuous counterpart with only a small number (say, 10) of discrete phases. Compared to the conventional continuous phase randomization case, where an infinite amount of random bits are required, our result shows that only a small amount (say, 4 bits) of randomness is needed.

Variational dynamics of the sub-Ohmic spin-boson model on the basis of multiple Davydov $\mathrm{D}_1$ states

Abstract: Dynamics of the sub-Ohmic spin-boson model is investigated by employing a multitude of the Davydov D$_1$ trial states, also known as the multi-D$_1$ Ansatz. Accuracy in dynamics simulations is improved significantly over the single D$_1$ Ansatz, especially in the weak system-bath coupling regime. The reliability of the multi-D$_1$ Ansatz for various coupling strengths and initial conditions are also systematically examined, with results compared closely with those of the hierarchy equations of motion and the path integral Monte Carlo approaches. In addition, a coherent-incoherent phase crossover in the nonequilibrium dynamics is studied through the multi-D$_1$ Ansatz. The phase diagram is obtained with a critical point $s_{c}=0.4$. For $s_{c}

Derivation of nonlinear Gibbs measures from many-body quantum mechanics

Abstract: We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and the interaction behaves as 1/T. We proceed by characterizing the interacting Gibbs state as minimizing a functional counting the free-energy relatively to the non-interacting case. We then perform an infinite-dimensional analogue of phase-space semiclassical analysis, using fine properties of the quantum relative entropy, the link between quantum de Finetti measures and upper/lower symbols in a coherent state basis, as well as Berezin-Lieb type inequalities. Our results cover the measure built on the defocusing nonlinear Schrodinger functional on a finite interval, as well as smoother interactions in dimensions d>1.

Entanglement entropy of squeezed vacua on a lattice

Abstract: We derive a formula for the entanglement entropy of squeezed states on a lattice in terms of the complex structure J. The analysis involves the identification of squeezed states with group-theoretical coherent states of the symplectic group and the relation between the coset Sp(2N,R)/Isot(J_0) and the space of complex structures. We present two applications of the new formula: (i) we derive the area law for the ground state of a scalar field on a generic lattice in the limit of small speed of sound, (ii) we compute the rate of growth of the entanglement entropy in the presence of an instability and show that it is bounded from above by the Kolmogorov-Sinai rate.

q-deformed noncommutative cat states and their nonclassical properties

Abstract: We study several classical-like properties of $q$-deformed nonlinear coherent states as well as nonclassical behaviors of $q$-deformed version of the Schr\"odinger cat states in noncommutative space. Coherent states in $q$-deformed space are found to be minimum uncertainty states together with the squeezed photon distributions unlike the ordinary systems, where the photon distributions are always Poissonian. Several advantages of utilizing cat states in noncommutative space over the standard quantum mechanical spaces have been reported here. For instance, the $q$-deformed parameter has been utilized to improve the squeezing of the quadrature beyond the ordinary case. Most importantly, the parameter provides an extra degree of freedom by which we achieve both quadrature squeezed and number squeezed cat states at the same time in a single system, which is impossible to achieve from ordinary cat states.

Gaussian optimizers and the additivity problem in quantum information theory

Abstract: This paper surveys two remarkable analytical problems of quantum information theory. The main part is a detailed report on the recent (partial) solution of the quantum Gaussian optimizer problem which establishes an optimal property of Glauber's coherent states -- a particular case of pure quantum Gaussian states. The notion of a quantum Gaussian channel is developed as a non-commutative generalization of an integral operator with Gaussian kernel, and it is shown that the coherent states, and under certain conditions only they, minimize a broad class of concave functionals of the output of a Gaussian channel. Thus, the output states corresponding to a Gaussian input are the `least chaotic', majorizing all the other outputs. The solution, however, is essentially restricted to the gauge-invariant case where a distinguished complex structure plays a special role. Also discussed is the related well-known additivity conjecture, which was solved in principle in the negative some five years ago. This refers to the additivity or multiplicativity (with respect to tensor products of channels) of information quantities related to the classical capacity of a quantum channel, such as the -norms or the minimal von Neumann or Renyi output entropies. A remarkable corollary of the present solution of the quantum Gaussian optimizer problem is that these additivity properties, while not valid in general, do hold in the important and interesting class of gauge-covariant Gaussian channels. Bibliography: 65 titles.

Bounds to precision for quantum interferometry with Gaussian states and operations

Abstract: We address high-precision measurements by active and passive interferometric schemes based on Gaussian states and operations. In particular, we look for the best states to be injected into their ports according to the quantum Cramer–Rao bound, i.e., maximizing the quantum Fisher information over all the involved parameters, given a constraint on the overall mean number of photons entering into the interferometer. We found that for passive interferometers involving only beam splitters, the optimal input leading to Heisenberg scaling is a pair of identical squeezed-coherent states with at most one-third of the total energy employed in squeezing. For active interferometers involving optical amplifiers, input coherent signals are enough to achieve Heisenberg scaling, given an optimal value of the amplification gain. For passive schemes our results clarify the role of squeezing in improving both the reference phase and the signal phase of an interferometer.

Two-way Gaussian quantum cryptography against coherent attacks in direct reconciliation

Abstract: We consider a two-way quantum cryptographic protocol with coherent states assuming direct reconciliation. A detailed security analysis is performed considering a two-mode coherent attack, which represents the residual eavesdropping once the parties have reduced the general attack by applying symmetric random permutations. In this context we provide a general analytical expression for the key rate, discussing the impact of the residual two-mode correlations on the security of the scheme. In particular, we identify the optimal eavesdropping against two-way quantum communication, which is given by a two-mode coherent attack with symmetric and separable correlations.

Spins Dynamics in a Dissipative Environment: Hierarchal Equations of Motion Approach Using a Graphics Processing Unit (GPU)

Abstract: A system with many energy states coupled to a harmonic oscillator bath is considered. To study quantum non-Markovian system-bath dynamics numerically rigorously and nonperturbatively, we developed a computer code for the reduced hierarchy equations of motion (HEOM) for a graphics processor unit (GPU) that can treat the system as large as 4096 energy states. The code employs a Pade spectrum decomposition (PSD) for a construction of HEOM and the exponential integrators. Dynamics of a quantum spin glass system are studied by calculating the free induction decay signal for the cases of 3 × 2 to 3 × 4 triangular lattices with antiferromagnetic interactions. We found that spins relax faster at lower temperature due to transitions through a quantum coherent state, as represented by the off-diagonal elements of the reduced density matrix, while it has been known that the spins relax slower due to suppression of thermal activation in a classical case. The decay of the spins are qualitatively similar regardless of ...

Entangled squeezed states in noncommutative spaces with minimal length uncertainty relations

Abstract: We provide an explicit construction of entangled states in a noncommutative space with nonclassical states, particularly with the squeezed states. Noncommutative systems are found to be more entangled than the usual quantum mechanical systems. The noncommutative parameter provides an additional degree of freedom in the construction by which one can raise the entanglement of the noncommutative systems to fairly higher values beyond the usual systems. Despite having classical-like behavior, coherent states in noncommutative space produce a small amount of entanglement and therefore they possess slight nonclassicality as well, which is not true for the coherent states of an ordinary harmonic oscillator.

Chaos in the Dicke model: quantum and semiclassical analysis

Abstract: The emergence of chaos in an atom-field system is studied employing both semiclassical and numerical quantum techniques, taking advantage of the algebraic character of the Hamiltonian. A semiclassical Hamiltonian is obtained by considering the expectation value of the quantum Hamiltonian in Glauber (for the field) and Bloch (for the atoms) coherent states. Regular and chaotic regions are identified by looking at the Poincare sections for different energies and parameter values. An analytical expression for the semiclassical energy density of states is obtained by integrating the available phase space, which provides an exact unfolding to extract the fluctuations in the level statistics. Quantum chaos is recognized in these fluctuations, as a function of the coupling strength, for different regions in the energy spectrum, evaluating the Anderson–Darling (A–D) parameter, which distinguishes the Wigner- or Poisson-like distributions. Peres lattices play a role similar to the Poincare section for quantum states. They are calculated employing efficient numerical solutions and are a powerful visual tool to identify individual states belonging to a regular or chaotic region, classified by utilizing the Poincare sections and the A–D parameter. Finally, the quantum Husimi function for selected excited states is shown to have a noticeable similitude with the Poincare sections at the same energy.

Quantum Hall effect in supersymmetric Chern-Simons theories

Abstract: We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantize the vortices and, by relating their dynamics to a matrix model, show that their ground state wave function is in the same universality class as the Laughlin state. We further construct coherent state representations of the excitations of a finite number of vortices. These are quasiholes. By an explicit computation of the Berry phase, without resorting to a plasma analogy, we show that these excitations have fractional charge and spin.