Fourier Phase Retrieval with a Single Mask by Douglas-Rachford Algorithm

Douglas-Rachford (DR) algorithm is analyzed for Fourier phase retrieval with a single random phase mask. Local, geometric convergence to a unique fixed point is proved with numerical demonstration of global convergence

DART-ID increases single-cell proteome coverage.

Analysis by liquid chromatography and tandem mass spectrometry (LC-MS/MS) can identify and quantify thousands of proteins in microgram-level samples, such as those comprised of thousands of cells. This process, however, remains challenging for smaller samples, such as the proteomes of single mammalian cells, because reduced protein levels reduce the number of confidently sequenced peptides. To alleviate this reduction, we developed Data-driven Alignment of Retention Times for IDentification (DART-ID). DART-ID implements principled Bayesian frameworks for global retention time (RT) alignment and for incorporating RT estimates towards improved confidence estimates of peptide-spectrum-matches. When applied to bulk or to single-cell samples, DART-ID increased the number of data points by 30-50% at 1% FDR, and thus decreased missing data. Benchmarks indicate excellent quantification of peptides upgraded by DART-ID and support their utility for quantitative analysis, such as identifying cell types and cell-type specific proteins. The additional datapoints provided by DART-ID boost the statistical power and double the number of proteins identified as differentially abundant in monocytes and T-cells. DART-ID can be applied to diverse experimental designs and is freely available at http://dart-id.slavovlab.net

Observing and Verifying the Quantum Trajectory of a Mechanical Resonator

Continuous weak measurement allows localizing open quantum systems in state space, and tracing out their quantum trajectory as they evolve in time. Efficient quantum measurement schemes have previously enabled recording quantum trajectories of microwave photon and qubit states. We apply these concepts to a macroscopic mechanical resonator, and follow the quantum trajectory of its motional state conditioned on a continuous optical measurement record. Starting with a thermal mixture, we eventually obtain coherent states of 78% purity--comparable to a displaced thermal state of occupation 0.14. We introduce a retrodictive measurement protocol to directly verify state purity along the trajectory, and furthermore observe state collapse and decoherence. This opens the door to measurement-based creation of advanced quantum states, and potential tests of gravitational decoherence models.Comment: 20 pages, 4 figure

Measurement-based quantum control of mechanical motion

Controlling a quantum system based on the observation of its dynamics is inevitably complicated by the backaction of the measurement process. Efficient measurements, however, maximize the amount of information gained per disturbance incurred. Real-time feedback then enables both canceling the measurement's backaction and controlling the evolution of the quantum state. While such measurement-based quantum control has been demonstrated in the clean settings of cavity and circuit quantum electrodynamics, its application to motional degrees of freedom has remained elusive. Here we show measurement-based quantum control of the motion of a millimetre-sized membrane resonator. An optomechanical transducer resolves the zero-point motion of the soft-clamped resonator in a fraction of its millisecond coherence time, with an overall measurement efficiency close to unity. We use this position record to feedback-cool a resonator mode to its quantum ground state (residual thermal occupation n = 0.29 +- 0.03), 9 dB below the quantum backaction limit of sideband cooling, and six orders of magnitude below the equilibrium occupation of its thermal environment. This realizes a long-standing goal in the field, and adds position and momentum to the degrees of freedom amenable to measurement-based quantum control, with potential applications in quantum information processing and gravitational wave detectors.Comment: New version with corrected detection efficiency as determined with a NIST-calibrated photodiode, added references and revised structure. Main conclusions are identical. 41 pages, 18 figure

Continuous Force and Displacement Measurement Below the Standard Quantum Limit

Quantum mechanics dictates that the precision of physical measurements must be subject to certain constraints. In the case of inteferometric displacement measurements, these restrictions impose a 'standard quantum limit' (SQL), which optimally balances the precision of a measurement with its unwanted backaction. To go beyond this limit, one must devise more sophisticated measurement techniques, which either 'evade' the backaction of the measurement, or achieve clever cancellation of the unwanted noise at the detector. In the half-century since the SQL was established, systems ranging from LIGO to ultracold atoms and nanomechanical devices have pushed displacement measurements towards this limit, and a variety of sub-SQL techniques have been tested in proof-of-principle experiments. However, to-date, no experimental system has successfully demonstrated an interferometric displacement measurement with sensitivity (including all relevant noise sources: thermal, backaction, and imprecision) below the SQL. Here, we exploit strong quantum correlations in an ultracoherent optomechanical system to demonstrate off-resonant force and displacement sensitivity reaching 1.5dB below the SQL. This achieves an outstanding goal in mechanical quantum sensing, and further enhances the prospects of using such devices for state-of-the-art force sensing applications.Comment: 18 pages, 7 figure