arXiv subjects

Ivan H. Deutsch

Publications and source records attributed to Ivan H. Deutsch.

At least 37 records · Page 2Linked to original sources

arXiv2020

Squeezing the angular momentum of an ensemble of complex multi-level atoms

Squeezing of collective atomic spins has been shown to improve the sensitivity of atomic clocks and magnetometers to levels significantly below the standard quantum limit. In most cases the requisite atom-atom entanglement has been generated by dispersive interaction with a quantized probe field, or by state dependent collisions in a quantum gas. Such experiments typically use complex multilevel atoms like Rb or Cs, with the relevant interactions designed so atoms behave like pseudo-spin-$1/2$ particles. We demonstrate the viability of spin squeezing for collective spins composed of the physical angular momenta of $\sim 10^6$ Cs atoms, each in an internal spin-4 hyperfine state. A peak metrological squeezing of $\gtrsim -5$dB was generated by quantum backaction from a dispersive quantum nondemolition (QND) measurement, implemented using a two-color optical probe that minimizes tensor light shifts without sacrificing measurement strength. Other significant developments include the successful application of composite pulse techniques for accurate dynamical control of the collective spin, enabled by broadband suppression of background magnetic fields inside a state-of-the-art magnetic shield. The absence of classical noise has allowed us to compare the observed quantum projection noise and squeezing to a theoretical model that properly accounts for both the relevant atomic physics and the spatial mode of the collective spin, finding good quantitative agreement and thereby validating its use in other contexts. Thus, our work sets the stage for experiments on quantum feedback, deterministic squeezing, closed-loop magnetometry, and new types of quantum simulation based on continuous QND measurement and feedback.

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arXiv2020

Simulation of complex dynamics of mean-field $p$-spin models using measurement-based quantum feedback control

We study the application of a new method for simulating nonlinear dynamics of many-body spin systems using quantum measurement and feedback [Muñoz-Arias et al., Phys. Rev. Lett. 124, 110503 (2020)] to a broad class of many-body models known as $p$-spin Hamiltonians, which describe Ising-like models on a completely connected graph with $p$-body interactions. The method simulates the desired mean field dynamics in the thermodynamic limit by combining nonprojective measurements of a component of the collective spin with a global rotation conditioned on the measurement outcome. We apply this protocol to simulate the dynamics of the $p$-spin Hamiltonians and demonstrate how different aspects of criticality in the mean-field regime are readily accessible with our protocol. We study applications including properties of dynamical phase transitions and the emergence of spontaneous symmetry breaking in the adiabatic dynamics of the collective spin for different values of the parameter $p$. We also demonstrate how this method can be employed to study the quantum-to-classical transition in the dynamics continuously as a function of system size.

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arXiv2020

Small, Highly Accurate Quantum Processor for Intermediate-Depth Quantum Simulations

Analog quantum simulation is widely considered a step on the path to fault tolerant quantum computation. If based on current noisy hardware, the accuracy of an analog simulator will degrade after just a few time steps, especially when simulating complex systems that are likely to exhibit quantum chaos. Here we describe a small, highly accurate quantum simulator and its use to run high fidelity simulations of three different model Hamiltonians for $>100$ time steps. While not scalable to exponentially large Hilbert spaces, this platform provides the accuracy and programmability required for systematic exploration of the interplay between dynamics, imperfections, and accuracy in quantum simulation.

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arXiv2020

Simulating nonlinear dynamics of collective spins via quantum measurement and feedback

We study a method to simulate quantum many-body dynamics of spin ensembles using measurement-based feedback. By performing a weak collective measurement on a large ensemble of two-level quantum systems and applying global rotations conditioned on the measurement outcome, one can simulate the dynamics of a mean-field quantum kicked top, a standard paradigm of quantum chaos. We analytically show that there exists a regime in which individual quantum trajectories adequately recover the classical limit, and show the transition between noisy quantum dynamics to full deterministic chaos described by classical Lyapunov exponents. We also analyze the effects of decoherence, and show that the proposed scheme represents a robust method to explore the emergence of chaos from complex quantum dynamics in a realistic experimental platform based on an atom-light interface.

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arXiv2019

Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice

We study the sampling complexity of a probability distribution associated with an ensemble ofidentical noninteracting bosons undergoing a quantum random walk on a one-dimensional lattice.With uniform nearest-neighbor hopping we show that one can efficiently sample the distribution fortimes logarithmic in the size of the system, while for longer times there is no known efficient samplingalgorithm. With time-dependent hopping and optimal control, we design the time evolution toapproximate an arbitrary Haar-random unitary map analogous to that designed for photons in alinear optical network. This approach highlights a route to generating quantum complexity byoptimal control only of a single-body unitary matrix. We study this in the context of two potentialexperimental realizations: a spinor optical lattice of ultracold atoms and a quantum gas microscope.

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arXiv2018

Optimal Pure-State Qubit Tomography via Sequential Weak Measurements

The spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space probabilities. We prove that this POVM is achieved by collectively measuring the spin projection of an ensemble of qubits weakly and isotropically. We apply this in the context of optimal tomography of pure qubits. We show numerically that through a sequence of weak measurements of random directions of the collective spin component, sampled discretely or in a continuous measurement with random controls, one can approach the optimal bound.

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arXiv2018

Enhanced cooperativity for quantum-nondemolition-measurement--induced spin squeezing of atoms coupled to a nanophotonic waveguide

We study the enhancement of cooperativity in the atom-light interface near a nanophotonic waveguide for application to quantum nondemolition (QND) measurement of atomic spins. Here the cooperativity per atom is determined by the ratio between the measurement strength and the decoherence rate. Counterintuitively, we find that by placing the atoms at an azimuthal position where the guided probe mode has the lowest intensity, we increase the cooperativity. This arises because the QND measurement strength depends on the interference between the probe and scattered light guided into an orthogonal polarization mode, while the decoherence rate depends on the local intensity of the probe. Thus, by proper choice of geometry, the ratio of good to bad scattering can be strongly enhanced for highly anisotropic modes. We apply this to study spin squeezing resulting from QND measurement of spin projection noise via the Faraday effect in two nanophotonic geometries, a cylindrical nanofiber and a square waveguide. We find that, with about 2500 atoms and using realistic experimental parameters, $ \sim 6.3 $ and $ \sim 13 $ dB of squeezing can be achieved on the nanofiber and square waveguide, respectively.

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arXiv2016

Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles

Symmetric ensembles of neutral atoms interacting via the Rydberg blockade are well-described by the Jaynes-Cummings Hamiltonian. We use this framework to study the problem of generating arbitrary superpositions of Dicke states of hyperfine qubits in such ensembles. The combination of the symmetric Rydberg blockade and microwaves that drive the qubits with a time-dependent phase is sufficient to make these ensembles completely controllable, in the sense that one can generate an arbitrary unitary transformation on the system. We apply this to the problem of state mapping. With currently feasible parameters, it is possible to generate arbitrary symmetric states of ~ 10 hypefine qubits with high fidelity in ~ 1 microsecond, assuming fast microwave phase switching times. To reduce the requirements on phase switching, we propose a "dressed ground control" scheme, in which the control task is simplified by restricting the system's dynamics to the dressed ground subspace.

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arXiv2016

Demonstration of the Jaynes-Cummings ladder with Rydberg-dressed atoms

We observe the nonlinearity of the Jaynes-Cummings (JC) ladder in the Autler-Townes spectroscopy of the hyperfine ground states for a Rydberg-dressed two-atom system. Here the role of the two-level system in the JC model is played by the presence or absence of a collective Rydberg excitation, and the bosonic mode manifests as the number $n$ of single atom spin flips, symmetrically distributed between the atoms. We measure the normal-mode splitting and $\sqrt{n}$ nonlinearity as a function of detuning and Rabi frequency, thereby experimentally establishing the isomorphism with the JC model.

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arXiv2016

Informational completeness in bounded-rank quantum-state tomography

We consider the problem of quantum-state tomography under the assumption that the state is pure, and more generally that its rank is bounded by a given value. In this scenario, new notions of informationally complete POVMs emerge, which allow for high-fidelity state estimation with fewer measurement outcomes than are required for an arbitrary rank state. We study this in the context of matrix completion, where the POVM outcomes determine only a few of the density matrix elements. We give an analytic solution that fully characterizes informational completeness and elucidates the important role that the positive-semidefinite property of density matrices plays in tomography. We show how positivity can impose a stricter notion of information completeness and allow us to use convex optimization programs to robustly estimate bounded-rank density matrices in the presence of statistical noise.

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arXiv2016

Dispersive response of atoms trapped near the surface of an optical nanofiber with applications to quantum nondemolition measurement and spin squeezing

We study the strong coupling between photons and atoms that can be achieved in an optical nanofiber geometry when the interaction is dispersive. While the Purcell enhancement factor for spontaneous emission into the guided mode does not reach the strong-coupling regime for individual atoms, one can obtain high cooperativity for ensembles of a few thousand atoms due to the tight confinement of the guided modes and constructive interference over the entire chain of trapped atoms. We calculate the dyadic Green's function, which determines the scattering of light by atoms in the presence of the fiber, and thus the phase shift and polarization rotation induced on the guided light by the trapped atoms. The Green's function is related to a full Heisenberg-Langevin treatment of the dispersive response of the quantized field to tensor polarizable atoms. We apply our formalism to quantum nondemolition (QND) measurement of the atoms via polarimetry. We study shot-noise-limited detection of atom number for atoms in a completely mixed spin state and the squeezing of projection noise for atoms in clock states. Compared with squeezing of atomic ensembles in free space, we capitalize on unique features that arise in the nanofiber geometry including anisotropy of both the intensity and polarization of the guided modes. We use a first principles stochastic master equation to model the squeezing as function of time in the presence of decoherence due to optical pumping. We find a peak metrological squeezing of ~5 dB is achievable with current technology for ~2500 atoms trapped 180 nm from the surface of a nanofiber with radius a=225 nm.

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arXiv2015

Quantum Tomography Protocols with Positivity are Compressed Sensing Protocols

Characterizing complex quantum systems is a vital task in quantum information science. Quantum tomography, the standard tool used for this purpose, uses a well-designed measurement record to reconstruct quantum states and processes. It is, however, notoriously inefficient. Recently, the classical signal reconstruction technique known as "compressed sensing" has been ported to quantum information science to overcome this challenge: accurate tomography can be achieved with substantially fewer measurement settings, thereby greatly enhancing the efficiency of quantum tomography. Here we show that compressed sensing tomography of quantum systems is essentially guaranteed by a special property of quantum mechanics itself---that the mathematical objects that describe the system in quantum mechanics are matrices with nonnegative eigenvalues. This result has an impact on the way quantum tomography is understood and implemented. In particular, it implies that the information obtained about a quantum system through compressed sensing methods exhibits a new sense of "informational completeness." This has important consequences on the efficiency of data taking for quantum tomography, and enables us to construct informationally complete measurements that are robust to noise and modeling errors. Moreover, our result shows that one can expand the numerical tool-box used in quantum tomography and employ highly efficient algorithms developed to handle large dimensional matrices on a large dimensional Hilbert space. While we mainly present our results in the context of quantum tomography, they apply to the general case of positive semidefinite matrix recovery.

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arXiv2015

Characterizing and Quantifying Quantum Chaos with Quantum Tomography

We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under application of the Floquet operator of a quantum map that possesses (or lacks) time reversal symmetry. We find that the rate of information gain, and hence the fidelity of quantum state reconstruction, depends on the symmetry class of the quantum map involved. Moreover, we find an increase in information gain and hence higher reconstruction fidelities when the Floquet maps employed increase in chaoticity. We make predictions for the information gain and show that these results are well described by random matrix theory in the fully chaotic regime. We derive analytical expressions for bounds on information gain using random matrix theory for different class of maps and show that these bounds are realized by fully chaotic quantum systems.

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arXiv2015

Robust quantum logic in neutral atoms via adiabatic Rydberg dressing

We study a scheme for implementing a controlled-Z (CZ) gate between two neutral-atom qubits based on the Rydberg blockade mechanism in a manner that is robust to errors caused by atomic motion. By employing adiabatic dressing of the ground electronic state, we can protect the gate from decoherence due to random phase errors that typically arise because of atomic thermal motion. In addition, the adiabatic protocol allows for a Doppler-free configuration that involves counterpropagating lasers in a $σ_+/σ_-$ orthogonal polarization geometry that further reduces motional errors due to Doppler shifts. The residual motional error is dominated by dipole-dipole forces acting on doubly-excited Rydberg atoms when the blockade is imperfect. For reasonable parameters, with qubits encoded into the clock states of $^{133}$Cs, we predict that our protocol could produce a CZ gate in $<10$ $μ$s with error probability on the order of $10^{-3}$.

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arXiv2014

Single Shot Quantum State Estimation via a Continuous Measurement in the Strong Backaction Regime

We study quantum tomography based on a stochastic continuous-time measurement record obtained from a probe field collectively interacting with an ensemble of identically prepared systems. In comparison to previous studies, we consider here the case in which the measurement-induced backaction has a nonnegligible effect on the dynamical evolution of the ensemble. We formulate a maximum likelihood estimate for the initial quantum state given only a single instance of the continuous diffusive measurement record. We apply our estimator to the simplest problem -- state tomography of a single pure qubit, which, during the course of the measurement, is also subjected to dynamical control. We identify a regime where the many-body system is well approximated at all times by a separable pure spin coherent state, whose Bloch vector undergoes a conditional stochastic evolution. We simulate the results of our estimator and show that we can achieve close to the upper bound of fidelity set by the optimal POVM. This estimate is compared to, and significantly outperforms, an equivalent estimator that ignores measurement backaction.

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arXiv2014

Quantum process tomography of unitary and near-unitary maps

We study quantum process tomography given the prior information that the map is a unitary or close to a unitary process. We show that a unitary map on a $d$-level system is completely characterized by a minimal set of $d^2{+}d$ elements associated with a collection of POVMs, in contrast to the $d^4{-}d^2$ elements required for a general completely positive trace-preserving map. To achieve this lower bound, one must probe the map with a particular set of $d$ pure states. We further compare the performance of different compressed sensing algorithms used to reconstruct a near-unitary process from such data. We find that when we have accurate prior information, an appropriate compressed sensing method reduces the required data needed for high-fidelity estimation, and different estimators applied to the same data are sensitive to different types of noise. Compressed sensing techniques can therefore be used both as indicators of error models and to validate the use of the prior assumptions.

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arXiv2013

Three-dimensional light-matter interface for collective spin squeezing in atomic ensembles

We study the three-dimensional nature of the quantum interface between an ensemble of cold, trapped atomic spins and a paraxial laser beam, coupled through a dispersive interaction. To achieve strong entanglement between the collective atomic spin and the photons, one must match the spatial mode of the collective radiation of the ensemble with the mode of the laser beam while minimizing the effects of decoherence due to optical pumping. For ensembles coupling to a probe field that varies over the extent of the cloud, the set of atoms that indistinguishably radiates into a desired mode of the field defines an inhomogeneous spin wave. Strong coupling of a spin wave to the probe mode is not characterized by a single parameter, the optical density, but by a collection of different effective atom numbers that characterize the coherence and decoherence of the system. To model the dynamics of the system, we develop a full stochastic master equation, including coherent collective scattering into paraxial modes, decoherence by local inhomogeneous diffuse scattering, and backaction due to continuous measurement of the light entangled with the spin waves. This formalism is used to study the squeezing of a spin wave via continuous quantum nondemolition (QND) measurement. We find that the greatest squeezing occurs in parameter regimes where spatial inhomogeneities are significant, far from the limit in which the interface is well approximated by a one-dimensional, homogeneous model.

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arXiv2013

Adiabatic quantum computation with Rydberg-dressed atoms

We study an architecture for implementing adiabatic quantum computation with trapped neutral atoms. Ground state atoms are dressed by laser fields in a manner conditional on the Rydberg blockade mechanism, thereby providing the requisite entangling interactions. As a benchmark we study the performance of a Quadratic Unconstrained Binary Optimization (QUBO) problem whose solution is found in the ground state spin configuration of an Ising-like model. We model a realistic architecture, including details of the atomic implementation, with qubits encoded into the clock states of 133Cs, effective B-fields implemented through stimulated Raman transitions, and atom-atom coupling achieved by excitation to the 100P3/2 Rydberg level. Including the fundamental effects of photon scattering, we find the fidelity of two-qubit implementation to be on the order of 0.99, with higher fidelities possible with improved laser sources.

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