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

ECONOMIC IMPORTANCE OF EXPORT-PRODUCING INDUSTRY IN MINNEAPOLIS-ST. PAUL METROPOLITAN REGION

Community/Rural/Urban Development, International Relations/Trade,

ECONOMIC IMPORTANCE OF EXPORT-PRODUCING INDUSTRY IN MINNESOTA

In this report, the role and importance of export-producing industries in Minnesota are discussed. Major emphasis is on agricultural-related industries and their economic importance to the State in value of gross output and contribution to gross state product.Community/Rural/Urban Development, International Relations/Trade,

ECONOMIC IMPORTANCE OF AGRICULTURE-RELATED INDUSTRY IN MINNESOTA

This report is the third in a series on interindustry and interregional relationships and their implications for the economy of Minnesota and its substate development regions. In this report, the role and importance of agriculture-related industries in Minnesota are discussed. A total of 19 agriculture and 35 food products manufacturing industries are identified as the principal agriculture-related industries in the state and the nation. Their interindustry and interregional (Minnesota and rest-of-nation) linkages are derived for the 1977 calendar year.Community/Rural/Urban Development,

Case studies of multi-day 3He-rich solar energetic particle periods

Context. Impulsive solar energetic particle events in the inner heliosphere show the long-lasting enrichment of 3He. Aims. We study the source regions of long-lasting 3He-rich solar energetic particle (SEP) events Methods. We located the responsible open magnetic field regions, we combined potential field source surface extrapolations (PFSS) with the Parker spiral, and compared the magnetic field of the identified source regions with in situ magnetic fields. The candidate open field regions are active region plages. The activity was examined by using extreme ultraviolet (EUV) images from the Solar Dynamics Observatory (SDO) and STEREO together with radio observations from STEREO and WIND. Results. Multi-day periods of 3He-rich SEP events are associated with ion production in single active region. Small flares or coronal jets are their responsible solar sources. We also find that the 3He enrichment may depend on the occurrence rate of coronal jets.Comment: 7page, 4 figure

EMPLOYMENT TRENDS AND PROJECTIONS FOR MINNESOTA AND ITS SUBSTATE DEVELOPMENT REGIONS

Labor and Human Capital,

USERS' GUIDE TO THE MINNESOTA REGIONAL DEVELOPMENT SIMULATION LABORATORY

This manual is a users' guide to the Minnesota Regional Development Simulation Laboratory, called SIMLAB.Community/Rural/Urban Development,