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

Riofrio, Carlos; Jessen, Poul; Deutsch, Ivan

doi:10.1088/0953-4075/44/15/154007

Cited by 23 publications

(38 citation statements)

References 31 publications

(126 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The minimally perturbative nature of the Faraday probe is ideal for quantum state estimation in cold atomic ensembles [21,22]. In this work we applied microwave control to null the quadratic Zeeman shift and minimize amplitude modulation of the Faraday signal.…”

Section: Discussionmentioning

confidence: 99%

“…Such polarization modulation is readily photodetected with a balanced polarimeter, and given knowledge of the gyromagnetic ratio yields calibration-free 'optical magnetometry', widely implemented in warm atomic vapors [20]. Faraday probes enable quantum state tomography of atomic gases, measuring a single spin projection in the laboratory frame while the spin state is evolved by applied radiofrequency and microwave fields [21,22], or by spin-mixing interactions in a degenerate spinor gas [3].…”

Section: A the Faraday Light-matter Interfacementioning

confidence: 99%

See 1 more Smart Citation

Continuous Faraday measurement of spin precession without light shifts

et al. 2017

View full text Add to dashboard Cite

We describe a dispersive Faraday optical probe of atomic spin which performs a weak measurement of spin projection of a quantum gas continuously for more than one second. To date focusing bright far-off-resonance probes onto quantum gases has proved invasive, due to strong scalar and vector light shifts exerting dipole and Stern-Gerlach forces. We show that tuning the probe near the magiczero wavelength at 790 nm between the fine-structure doublet of 87 Rb cancels the scalar light shift, and careful control of polarization eliminates the vector light shift. Faraday rotations due to each fine-structure line reinforce at this wavelength, enhancing the signal-to-noise ratio for a fixed rate of probe-induced decoherence. Using this minimally-invasive spin probe we perform microscale atomic magnetometry at high temporal resolution. Spectrogram analysis of the Larmor precession signal of a single spinor Bose-Einstein condensate measures a time-varying magnetic field strength with 1 µG accuracy every 5 ms; or equivalently makes > 200 successive measurements each at 10 pT/ √ Hz sensitivity.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: A the Faraday Light-matter Interfacementioning

confidence: 99%

Continuous Faraday measurement of spin precession without light shifts

et al. 2017

View full text Add to dashboard Cite

show abstract

“…In this backaction-free approximation, the tomographic estimate for the initial stateρ(0) reduces to a standard problem of constrained maximum likelihood [4].…”

Section: Spin Estimation Through Polarization Spectrocopymentioning

confidence: 99%

“…Following the work of Riofrío et al [4], we choose a control Hamiltonian, H c (t), that is randomized between a set of operators that rapidly generates the group of SU (2) rotations,…”

Section: Estimating the State Of A Pure Qubitmentioning

confidence: 99%

Single-shot quantum state estimation via a continuous measurement in the strong backaction regime

2014

View full text Add to dashboard Cite

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.

show abstract

“…Besides the control phases, H C (t) depends on the following parameters (nominal values in parenthesis): the Larmor frequency in the bias field (Ω 0 = 2π × 1MHz), the rf Larmor frequencies in the rotating frame (Ω x = Ω y = 2π × 25kHz), the µw Rabi frequency (Ω µw = 27.5kHz), and the rf and µw detunings from resonance (∆ rf = ∆ µw = 0). For details see [22] and the accompanying supplemental material.…”

mentioning

confidence: 99%

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

et al. 2015

View full text Add to dashboard Cite

Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant inputoutput maps are unitary transformations, and the fundamental challenge becomes how to implement these with high fidelity in the presence of experimental imperfections and decoherence. For two-level systems (qubits) most aspects of unitary control are well understood, but for systems with Hilbert space dimension d>2 (qudits), many questions remain regarding the optimal design of control Hamiltonians 1 and the feasibility of robust implementation 2,3 . Here we show that arbitrary, randomly chosen unitary transformations can be efficiently designed and implemented in a large dimensional Hilbert space (d=16) associated with the electronic ground state of atomic 133 Cs, 4 achieving fidelities above 0.98 as measured by randomized benchmarking 5 . Generalizing the concepts of inhomogeneous control 6 and dynamical decoupling 7 to d>2 systems, we further demonstrate that these qudit unitary maps can be made robust to both static and dynamic perturbations. Potential applications include improved fault-tolerance in universal quantum computation 8 , nonclassical state preparation for high-precision metrology 9 , implementation of quantum simulations 10 , and the study of fundamental physics related to open quantum systems and quantum chaos 11 .The goal of quantum control is to perform a desired transformation through dynamical evolution driven by a control Hamiltonian H C (t) . For example, one common objective is to evolve the system from a known initial state to a desired final state. If the control task is simple or special symmetries are present, it is sometimes possible to find a high-performing control Hamiltonian through intuition, or to construct one using group theoretic methods 12 . In this letter we explore the use of "optimal control" 1 to design control Hamiltonians for tasks of varying complexity, from state-to-state maps to unitary maps on the entire accessible Hilbert space. The basic procedure is well established: the Hamiltonian H C (t) is parameterized by a set of control variables, and a numerical search is performed to find values that optimize the fidelity with which the control objective is achieved. The application of optimal control to quantum systems originated in NMR 13 and physical chemistry 1 , and has since expanded to include, e. g., ultrafast physics 14 , cold atoms 15,16 , biological molecules 17 , spins in condensed matter 18 , and superconducting circuits 19 .We study the efficacy of numerical design and the performance of the resulting control Hamiltonians using a well developed testbed consisting of the electron and nuclear spins of individual 133 Cs atoms driven by radiofrequency (rf) and microwave (µw) magnetic fields (Fig. 1) 16 . Our experiments show that the optimal control strategy is adaptable to a wide range of control tasks, and that it can generate control Hamiltonians with excellent performance even in the prese...

show abstract

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

Cited by 23 publications

References 31 publications

Continuous Faraday measurement of spin precession without light shifts

Continuous Faraday measurement of spin precession without light shifts

Single-shot quantum state estimation via a continuous measurement in the strong backaction regime

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

Contact Info

Product

Resources

About