arXiv subjects

Klaus Molmer

Publications and source records attributed to Klaus Molmer.

At least 19 recordsLinked to original sources

arXiv2024

Generating Einstein$\unicode{x2013}$Podolsky$\unicode{x2013}$Rosen correlations for teleporting collective spin states in a two dimensional trapped ion crystal

We propose the use of phonon$\unicode{x2013}$mediated interactions as an entanglement resource to engineer Einstein$\unicode{x2013}$Podolsky$\unicode{x2013}$Rosen (EPR) correlations and to perform teleportation of collective spin states in two$\unicode{x2013}$dimensional ion crystals. We emulate continuous variable quantum teleportation protocols between subsystems corresponding to different nuclear spin degrees of freedom. In each of them, a quantum state is encoded in an electronic spin degree of freedom that couples to the vibrational modes of the crystal. We show that high fidelity teleportation of spin-coherent states and their phase-displaced variant, entangled spin-squeezed states, and Dicke states, is possible for realistic experimental conditions in arrays from a few tens to a few hundred ions.

quant-ph↗

arXiv2020

Estimating a fluctuating magnetic field with a continuously monitored atomic ensemble

We study the problem of estimating a time dependent magnetic field by continuous optical probing of an atomic ensemble. The magnetic field is assumed to follow a stochastic Ornstein-Uhlenbeck process and it induces Larmor precession of the atomic ground state spin, which is read out by the Faraday polarization rotation of a laser field probe. The interactions and the measurement scheme are compatible with a hybrid quantum-classical Gaussian description of the unknown magnetic field, and the atomic and field variables. This casts the joint conditional quantum dynamics and classical parameter estimation problem in the form of update formulas for the first and second moments of the classical and quantum degrees of freedom. Our hybrid quantum-classical theory is equivalent with the classical theory of Kalman filtering and with the quantum theory of Gaussian states. By reference to the classical theory of smoothing and with the quantum theory of past quantum states, we show how optical probing after time $t$ improves our estimate of the value of the magnetic field at time $t$, and we present numerical simulations that analyze and explain the improvement over the conventional filtering approach.

quant-ph↗

arXiv2018

The quantum regression theorem for out-of-time-ordered correlation functions

We derive an extension of the quantum regression theorem to calculate out-of-time-order correlation functions in Markovian open quantum systems. While so far mostly being applied in the analysis of many-body physics, we demonstrate that out-of-time-order correlation functions appear naturally in optical detection schemes with interferometric delay lines, and we apply our extended quantum regression theorem to calculate the non-trivial photon counting fluctuations in split and recombined signals from a quantum light source.

quant-ph↗

arXiv2017

How many atoms get excited when they decay?

We analyze the time evolution of a two-level system prepared in a superposition of its ground state and radiatively unstable excited state. We show that by choosing appropriate means of detection of the radiated field, we can steer the evolution of the emitter and herald its preparation in the fully excited state. We determine the probability for the occurrence of this "excitation during the decay" of a remote emitter.

quant-ph↗

arXiv2016

Single-atom single-photon coupling facilitated by atomic-ensemble dark-state mechanisms

We propose to couple single atomic qubits to photons incident on a cavity containing an atomic ensemble of a different species that mediates the coupling via Rydberg interactions. Subject to a classical field and the cavity field, the ensemble forms a collective dark state which is resonant with the input photon, while excitation of a qubit atom leads to a secondary "dark" state that splits the cavity resonance. The two different dark state mechanisms yield zero and $π$ reflection phase shifts and can be used to implement quantum gates between atomic and optical qubits.

quant-ph↗

arXiv2015

Hypothesis testing with open quantum systems

Using a quantum circuit model we derive the maximal ability to distinguish which of several candidate Hamiltonians describe an open quantum system. This theory, in particular, provides the maximum information retrievable from continuous quantum measurement records, available when a quantum system is perturbatively coupled to a broadband quantized environment.

quant-ph↗

arXiv2014

Dissipative Landau-Zener level crossing subject to continuous measurement: Excitation despite decay

The Landau-Zener formula provides an analytical expression for the final excitation of a quantum system after passage of an avoided crossing of two energy levels. If the two levels correspond to a ground state, and to an excited state which is subject to radiative decay, the probability of exciting the system by adiabatic passage of the level crossing is reduced. In this article we use a stochastic master equation to study the level crossing dynamics when the system is subject to continuous probing of the emitted radiation. The measurement backaction on the system associated with the fluctuating homodyne detection record alters the level crossing dynamics, leading to significant excitation in spite of decay and imperfect transfer.

quant-ph↗

arXiv2013

Stimulated adiabatic passage in a dissipative Rydberg superatom

We study two-photon excitation of Rydberg states of atoms under stimulated adiabatic passage with delayed laser pulses. We find that the combination of strong interaction between the atoms in Rydberg state and the spontaneous decay of the intermediate exited atomic state leads to the Rydberg excitation of precisely one atom within the atomic ensemble. The quantum Zeno effect offers a lucid interpretation of this result: the Rydberg blocked atoms repetitively scattering photons effectively monitor a randomly excited atom which therefore remains in the Rydberg state. This system can be used for deterministic creation and, possibly, extraction of Rydberg atoms or ions one at a time. The sympathetic monitoring via decay of ancilla particles may find wider applications for state preparation and probing of interactions in dissipative many-body systems.

quant-ph↗

arXiv2012

Universal properties of Fermi gases in arbitrary dimensions

We consider spin-1/2 Fermi gases in arbitrary, integer or non-integer spatial dimensions, interacting via a Dirac delta potential. We first generalize the method of Tan's distributions and implement short-range boundary conditions to arbitrary dimension and we obtain a set of universal relations for the Fermi gas. Three-dimensional scattering under very general conditions of transversal confinement is described by an effectively reduced-dimensional scattering length, which we show depends on the three-dimensional scattering length in a universal way. Our formula for non-integer dimensions interpolates between the known results in integer dimensions 1, 2 and 3. Without any need to solve the associated multichannel scattering problem, we find that confinement-induced resonances occur in all dimensions different from D=2, while reduced-dimensional contacts, related to the tails of the momentum distributions, are connected to the three-dimensional contact by a correction factor of purely geometric origin.

hep-th↗

arXiv2011

Universal relations for the two-dimensional spin-1/2 Fermi gas with contact interactions

We present universal relations for a two-dimensional Fermi gas with pairwise contact interactions. The derivation of these relations is made possible by obtaining the explicit form of a generalized function -- selector -- in the momentum representation. The selector implements the short-distance boundary condition between two fermions in a straightforward manner, and leads to simple derivations of the universal relations, in the spirit of Tan's original method for the three-dimensional gas.

cond-mat.quant-gas↗

arXiv2011

Sympathetic Wigner function tomography of a dark trapped ion

A protocol is provided to reconstruct the Wigner function for the motional state of a trapped ion via fluorescence detection on another ion in the same trap. This "sympathetic tomography" of a dark ion without optical transitions suitable for state measurements is based on the mapping of its motional state onto one of the collective modes of the ion pair. The quantum state of this vibrational eigenmode is subsequently measured through sideband excitation of the bright ion. Physical processes to implement the desired state transfer and read-out are derived, and the accomplishment of the scheme for different mass ratios is evaluated.

quant-ph↗

arXiv2011

Quasi-one-dimensional scattering in a discrete model

We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero Bloch quasi- momenta, considering as well finite sizes and transversal traps that support a continuum of states. This is made straightforward by using the exact ansatz for the quasi-one-dimensional states from the beginning. In the more interesting case of genuine two-particle scattering, we find that more than one confinement-induced resonance appear due to the non-separability of the center-of-mass and relative coordinates on the lattice. This is done by solving its corresponding Lippmann- Schwinger-like equation. We characterize the effective one-dimensional interaction and compare it with a model that includes only the effect of the dominant, broadest resonance, which amounts to a single-pole approximation for the interaction coupling constant.

quant-ph↗

arXiv2011

Efficient Grover search with Rydberg blockade

We present efficient methods to implement the quantum computing Grover search algorithm using the Rydberg blockade interaction. We show that simple pi-pulse excitation sequences between ground and Rydberg excited states readily produce the key conditional phase shift and inversion-about-the mean unitary operations for the Grover search. Multi-qubit implementation schemes suitable for different properties of the atomic interactions are identifed and the error scaling of the protocols with system size is found to be promising for immediate experimental investigation.

quant-ph↗

arXiv2009

Cooling a micro-mechanical resonator to its ground state by measurement back-action

We present an analysis of the cooling of a micro-mechanical resonator by means of measurements and back action. The measurements are performed via the coupling to a Cooper-pair box, and although the coupling does not lead to net cooling, the extraction of information and hence entropy from the system leads to a pure quantum state. Under suitable circumstances, the states become very close to coherent states, conditioned on the measurement record, and can hence be displaced to the oscillator ground state.

quant-ph↗

arXiv2009

Dynamical programming of continuously observed quantum systems

We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes, which correspond respectively to deterministic and stochastic Master Equation dynamics. For the quantum feedback control scheme with continuous non-demolition observations we exploit the separation theorem of filtering and control aspects for quantum stochastic dynamics to derive a generalized Hamilton-Jacobi-Bellman equation. If the control is restricted to only Hamiltonian terms this is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term. In this work, we consider, in particular, the case when control is restricted to only observation. A controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure state from a mixed state of a quantum two-level system.

quant-ph↗

arXiv2009

Quantum learning by measurement and feedback

We propose an approach to quantum computing in which quantum gate strengths are parametrized by quantum degrees of freedom, and the capability of the quantum computer to perform desired tasks is monitored and gradually improved by successive feedback modifications of the coupling strength parameters. Our proposal aims at experimental implementation, scalable to computational problems too large to be simulated theoretically, and we demonstrate feasibility of our proposal with simulations on search and factoring algorithms.

quant-ph↗

arXiv2008

Atomic quantum superposition state generation via optical probing

We analyze the performance of a protocol to prepare an atomic ensemble in a superposition of two macroscopically distinguishable states. The protocol relies on conditional measurements performed on a light field, which interacts with the atoms inside an optical cavity prior to detection, and we investigate cavity enhanced probing with continuous beams of both coherent and squeezed light. The stochastic master equations used in the analysis are expressed in terms of the Hamiltonian of the probed system and the interaction between the probed system and the probe field and are thus quite generally applicable.

quant-ph↗

arXiv2008

Quantum fluctuations in the image of a Bose gas

We analyze the information content of density profiles for an ultracold Bose gas of atoms and extract resolution limits for observables contained in these images. Our starting point is density correlations that we compute within the Bogoliubov approximation, taking into account quantum and thermal fluctuations beyond mean-field theory. This provides an approximate way to construct the joint counting statistics of atoms in an array of pixels covering the gas. We derive the Fisher information of an image and the associated Cramer-Rao sensitivity bound for measuring observables contained in the image. We elaborate on our recent study on position measurements of a dark soliton [Negretti et al., Phys. Rev. A 77, 043606 (2008)] where a sensitivity scaling with the atomic density as n^{-3/4} was found. We discuss here a wider class of soliton solutions and present a detailed analysis of the Bogoliubov excitations and the gapless (Goldstone) excitation modes. These fluctuations around the mean field contribute to the noise in the image, and we show how they can actually improve the ability to locate the position of the soliton.

quant-ph↗