arXiv subjects

Ivan H. Deutsch

Publications and source records attributed to Ivan H. Deutsch.

At least 55 records · Page 3Linked to original sources

arXiv2013

Robust site-resolved quantum gates in an optical lattice via inhomogeneous control

Ultracold atoms in optical lattices are an important platform for quantum information science, lending itself naturally to quantum simulation of many-body physics and providing a possible path towards a scalable quantum computer. To realize its full potential, atoms at individual lattice sites must be accessible to quantum control and measurement. This challenge has so far been met with a combination of high-resolution microscopes and resonance addressing that have enabled both site-resolved imaging and spin-flips. Here we show that methods borrowed from the field of inhomogeneous control can greatly increase the performance of resonance addressing in optical lattices, allowing us to target arbitrary single-qubit gates on desired sites, with minimal crosstalk to neighboring sites and greatly improved robustness against uncertainty in the lattice position. We further demonstrate the simultaneous implementation of different gates at adjacent sites with a single global control waveform. Coherence is verified through two-pulse Ramsey interrogation, and randomized benchmarking is used to measure an average gate fidelity of ~95%. Our control-based approach to reduce crosstalk and increase robustness is broadly applicable in optical lattices irrespective of geometry, and may be useful also on other platforms for quantum information processing, such as ion traps and nitrogen-vacancy centers in diamond.

quant-ph↗

arXiv2013

Information gain in tomography - A quantum signature of chaos

We find quantum signatures of classical chaos in various metrics of information gain in quantum tomography. We employ a quantum state estimator based on weak collective measurements of an ensemble of identically prepared systems. The tomographic measurement record consists of a sequence of expectation values of a Hermitian operator that evolves under repeated application of the Floquet map of the quantum kicked top. We find an increase in information gain and hence higher fidelities in the reconstruction algorithm when the chaoticity parameter map increases. The results are well predicted by random matrix theory.

quant-ph↗

arXiv2012

Enhanced squeezing of a collective spin via control of its qudit subsystems

Unitary control of qudits can improve the collective spin squeezing of an atomic ensemble. Preparing the atoms in a state with large quantum fluctuations in magnetization strengthens the entangling Faraday interaction. The resulting increase in interatomic entanglement can be converted into metrologically useful spin squeezing. Further control can squeeze the internal atomic spin without compromising entanglement, providing an overall multiplicative factor in the collective squeezing. We model the effects of optical pumping and study the tradeoffs between enhanced entanglement and decoherence. For realistic parameters we see improvements of ~10 dB.

quant-ph↗

arXiv2011

Orbital order of spinless fermions near an optical Feshbach resonance

We study the quantum phases of a three-color Hubbard model that arises in the dynamics of the p-band orbitals of spinless fermions in an optical lattice. Strong, color-dependent interactions are induced by an optical Feshbach resonance. Starting from the microscopic scattering properties of ultracold atoms, we derive the orbital exchange constants at 1/3 filling on the cubic optical lattice. Using this, we compute the phase diagram in a Gutzwiller ansatz. We find novel phases with 'axial orbital order' in which pz and px + ipy (or px - ipy) orbitals alternate.

cond-mat.quant-gas↗

arXiv2011

Control of inhomogeneous atomic ensembles of hyperfine qudits

We study the ability to control d-dimensional quantum systems (qudits) encoded in the hyperfine spin of alkali-metal atoms through the application of radio- and microwave-frequency magnetic fields in the presence of inhomogeneities in amplitude and detuning. Such a capability is essential to the design of robust pulses that mitigate the effects of experimental uncertainty and also for application to tomographic addressing of particular members of an extended ensemble. We study the problem of preparing an arbitrary state in the Hilbert space from an initial fiducial state. We prove that inhomogeneous control of qudit ensembles is possible based on a semi-analytic protocol that synthesizes the target through a sequence of alternating rf and microwave-driven SU(2) rotations in overlapping irreducible subspaces. Several examples of robust control are studied, and the semi-analytic protocol is compared to a brute force, full numerical search. For small inhomogeneities, < 1%, both approaches achieve average fidelities greater than 0.99, but the brute force approach performs superiorly, reaching high fidelities in shorter times and capable of handling inhomogeneities well beyond experimental uncertainty. The full numerical search is also applied to tomographic addressing whereby two different nonclassical states of the spin are produced in two halves of the ensemble.

quant-ph↗

arXiv2010

Quantum tomography of the full hyperfine manifold of atomic spins via continuous measurement on an ensemble

Quantum state reconstruction based on weak continuous measurement has the advantage of being fast, accurate, and almost non-perturbative. In this work we present a pedagogical review of the protocol proposed by Silberfarb et al., PRL 95 030402 (2005), whereby an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner so as to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time through a maximum-likelihood estimate. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sublevels of a large-spin alkali atom, 133Cs. We detail two different protocols for control. Using magnetic interactions and a quadratic ac-Stark shift, we can reconstruct a chosen hyperfine manifold F, e.g., the 7-dimensional F=3 manifold in the electronic-ground state of Cs. We review the procedure as implemented in experiments (Smith et al., PRL 97 180403 (2006)). We extend the protocol to the more ambitious case of reconstruction of states in the full 16-dimensional electronic-ground subspace (F=3 \oplus F=4), controlled by microwaves and radio-frequency magnetic fields. We give detailed derivations of all physical interactions, approximations, numerical methods, and fitting procedures, tailored to the realistic experimental setting. For the case of light-shift and magnetic control, reconstruction fidelities of \sim 0.95 have been achieved, limited primarily by inhomogeneities in the light shift. For the case of microwave/RF-control we simulate fidelity >0.97, limited primarily by signal-to-noise.

quant-ph↗

arXiv2010

Strongly Enhanced Spin Squeezing via Quantum Control

We describe a new approach to spin squeezing based on a double-pass Faraday interaction between an optical probe and an optically dense atomic sample. A quantum eraser is used to remove residual spin-probe entanglement, thereby realizing a single-axis twisting unitary map on the collective spin. This interaction can be phase-matched, resulting in exponential enhancement of squeezing. In practice the scaling and peak squeezing depends on decoherence, technical loss, and noise. A simplified model indicates ~10 dB of squeezing should be achievable with current laboratory parameters.

quant-ph↗

arXiv2009

Random unitary maps for quantum state reconstruction

We study the possibility of performing quantum state reconstruction from a measurement record that is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of a single random unitary map, U_0. We show that while this single-parameter orbit in operator space is not informationally complete, it can be used to yield surprisingly high-fidelity reconstruction. For a d-dimensional Hilbert space with the initial observable in su(d), the measurement record lacks information about a matrix subspace of dimension > d-2 out of the total dimension d^2-1. We determine the conditions on U_0 such that the bound is saturated, and show they are achieved by almost all pseudorandom unitary matrices. When we further impose the constraint that the physical density matrix must be positive, we obtain even higher fidelity than that predicted from the missing subspace. With prior knowledge that the state is pure, the reconstruction will be perfect (in the limit of vanishing noise) and for arbitrary mixed states, the fidelity is over 0.96, even for small d, and reaching F > 0.99 for d > 9. We also study the implementation of this protocol based on the relationship between random matrices and quantum chaos. We show that the Floquet operator of the quantum kicked top provides a means of generating the required type of measurement record, with implications on the relationship between quantum chaos and information gain.

quant-ph↗

arXiv2009

Quantum control and measurement of atomic spins in polarization spectroscopy

Quantum control and measurement are two sides of the same coin. To affect a dynamical map, well-designed time-dependent control fields must be applied to the system of interest. To read out the quantum state, information about the system must be transferred to a probe field. We study a particular example of this dual action in the context of quantum control and measurement of atomic spins through the light-shift interaction with an off-resonant optical probe. By introducing an irreducible tensor decomposition, we identify the coupling of the Stokes vector of the light field with moments of the atomic spin state. This shows how polarization spectroscopy can be used for continuous weak measurement of atomic observables that evolve as a function of time. Simultaneously, the state-dependent light shift induced by the probe field can drive nonlinear dynamics of the spin, and can be used to generate arbitrary unitary transformations on the atoms. We revisit the derivation of the master equation in order to give a unified description of spin dynamics in the presence of both nonlinear dynamics and photon scattering. Based on this formalism, we review applications to quantum control, including the design of state-to-state mappings, and quantum-state reconstruction via continuous weak measurement on a dynamically controlled ensemble.

quant-ph↗

arXiv2009

Controlling nuclear spin exchange via optical Feshbach resonances in ${}^{171}$Yb

Nuclear spin exchange occurs in ultracold collisions of fermionic alkaline-earth-like atoms due to a difference between s- and p-wave phase shifts. We study the use of an optical Feshbach resonance, excited on the ${}^1S_0 \to {}^3P_1$ intercombination line of ${}^{171}$Yb, to affect a large modification of the s-wave scattering phase shift, and thereby optically mediate nuclear exchange forces. We perform a full multichannel calculation of the photoassociation resonances and wave functions and from these calculate the real and imaginary parts of the scattering length. As a figure of merit of this interaction, we estimate the fidelity to implement a $\sqrt{SWAP}$ entangling quantum logic gate for two atoms trapped in the same well of an optical lattice. For moderate parameters one can achieve a gate fidelity of $\sim95% $ in a time of $\sim 50 μ$s.

quant-ph↗

arXiv2009

Coherent control of atomic transport in spinor optical lattices

Coherent transport of atoms trapped in an optical lattice can be controlled by microwave-induced spin flips that correlate with site-to-site hopping. We study the controllability of homogeneous one-dimensional systems of noninteracting atoms in the absence of site addressability. Given these restrictions, we construct a deterministic protocol to map an initially localized Wannier state to a wave packet that that is coherently distributed over n sites. This is extended to analytic solutions for arbitrary unitary maps given homogenous systems and in the presence of time-dependent uniform forces. Such control is important for applications in quantum information processing such as quantum computing and quantum simulations of condensed matter phenomena.

quant-ph↗

arXiv2009

Constructing General Unitary Maps from State Preparations

We present an efficient algorithm for generating unitary maps on a $d$-dimensional Hilbert space from a time-dependent Hamiltonian through a combination of stochastic searches and geometric construction. The protocol is based on the eigen-decomposition of the map. A unitary matrix can be implemented by sequentially mapping each eigenvector to a fiducial state, imprinting the eigenphase on that state, and mapping it back to the eigenvector. This requires the design of only $d$ state-to-state maps generated by control waveforms that are efficiently found by a gradient search with computational resources that scale polynomially in $d$. In contrast, the complexity of a stochastic search for a single waveform that simultaneously acts as desired on all eigenvectors scales exponentially in $d$. We extend this construction to design maps on an $n$-dimensional subspace of the Hilbert space using only $n$ stochastic searches. Additionally, we show how these techniques can be used to control atomic spins in the ground electronic hyperfine manifold of alkali atoms in order to implement general qudit logic gates as well to perform a simple form of error correction on an embedded qubit.

quant-ph↗

arXiv2008

Quantum control of the hyperfine-coupled electron and nuclear spins in alkali atoms

We study quantum control of the full hyperfine manifold in the ground-electronic state of alkali atoms based on applied radio frequency and microwave fields. Such interactions should allow essentially decoherence-free dynamics and the application of techniques for robust control developed for NMR spectroscopy. We establish the conditions under which the system is controllable in the sense that one can generate an arbitrary unitary on the system. We apply this to the case of $^{133}$Cs with its $d=16$ dimensional Hilbert space of magnetic sublevels in the $6S_{1/2}$ state, and design control waveforms that generate an arbitrary target state from an initial fiducial state. We develop a generalized Wigner function representation for this space consisting of the direct sum of two irreducible representation of SU(2), allowing us to visualize these states. The performance of different control scenarios is evaluated based on the ability to generate high-fidelity operation in an allotted time with the available resources. We find good operating points commensurate with modest laboratory requirements.

quant-ph↗

arXiv2008

Analytic models of ultra-cold atomic collisions at negative energies for application to confinement-induced resonances

We construct simple analytic models of the $S$-matrix, accounting for both scattering resonances and smooth background contributions for collisions that occur below the s-wave threshold. Such models are important for studying confinement-induced resonances such as those occurring in cold collisions of $^{133}$Cs atoms in separated sites of a polarization-gradient optical lattice. Because these resonances occur at negative energy with respect to the s-wave threshold, they cannot be studied easily using direct numerical solutions of the Schrödinger equation. Using our analytic model, we extend previous studies of negative-energy scattering to the multichannel case, accounting for the interplay of Feshbach resonances, large background scattering lengths, and inelastic processes.

physics.atom-ph↗

arXiv2008

Sideband cooling while preserving coherences in the nuclear spin state in group-II-like atoms

We propose a method for laser cooling group-II-like atoms without changing the quantum state of their nuclear spins, thus preserving coherences that are usually destroyed by optical pumping. As group-II-like atoms have a $^1S_0$ closed-shell ground state, nuclear spin and electronic degrees of freedom are decoupled, allowing for independent manipulation. The hyperfine interaction that couples these degrees of freedom in excited states can be suppressed through the application of external magnetic fields. Our protocol employs resolved-sideband cooling on the forbidden clock transition, $^1S_0 \to {}^3P_0$, with quenching via coupling to the rapidly decaying $^1P_1$ state, deep in the Paschen-Back regime. This makes it possible to laser cool neutral atomic qubits without destroying the quantum information stored in their nuclear spins, as shown in two examples, $^{171}$Yb and $^{87}$Sr.

quant-ph↗

arXiv2007

Quantum Control of the Hyperfine Spin of a Cs Atom Ensemble

We demonstrate quantum control of a large spin-angular momentum associated with the F=3 hyperfine ground state of 133Cs. A combination of time dependent magnetic fields and a static tensor light shift is used to implement near-optimal controls and map a fiducial state to a broad range of target states, with yields in the range 0.8-0.9. Squeezed states are produced also by an adiabatic scheme that is more robust against errors. Universal control facilitates the encoding and manipulation of qubits and qudits in atomic ground states, and may lead to improvement of some precision measurements.

quant-ph↗

arXiv2006

A quasi-Hermitian pseudopotential for higher partial wave scattering

We formulate a new quasi-Hermitian delta-shell pseudopotential for higher partial wave scattering, and show that any such potential must have an energy-dependent regularization. The quasi-Hermiticity of the Hamiltonian leads to a complete set of biorthogonal wave functions that can be used as a basis to expand and diagonalize other two-body Hamiltonians. We demonstrate this procedure for the case of ultracold atoms in a polarization-gradient optical lattice, interacting pairwise when two atoms are transported together from separated lattice sites. Here the pseudopotential depends explicitly on the trapping potential. Additionally, we calculate the location of trap-induced resonances for higher partial waves, which occur when a molecular eigenstate is shifted to resonance with a trap eigenstate. We verify the accuracy of the pseudopotential approach using a toy model in which a square well acts as the true interaction potential, and see excellent agreement.

quant-ph↗

arXiv2006

Efficient Quantum State Estimation by Continuous Weak Measurement and Dynamical Control

We demonstrate a fast, robust and non-destructive protocol for quantum state estimation based on continuous weak measurement in the presence of a controlled dynamical evolution. Our experiment uses optically probed atomic spins as a testbed, and successfully reconstructs a range of trial states with fidelities of ~90%. The procedure holds promise as a practical diagnostic tool for the study of complex quantum dynamics, the testing of quantum hardware, and as a starting point for new types of quantum feedback control.

quant-ph↗