69 research outputs found
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
Polarimetric analysis of stress anisotropy in nanomechanical silicon nitride resonators
We realise a circular gray-field polariscope to image stress-induced
birefringence in thin (submicron thick) silicon nitride (SiN) membranes and
strings. This enables quantitative mapping of the orientation of principal
stresses and stress anisotropy, complementary to, and in agreement with, finite
element modeling (FEM). Furthermore, using a sample with a well known stress
anisotropy, we extract a new value for the photoelastic (Brewster) coefficient
of silicon nitride, .
We explore possible applications of the method to analyse and quality-control
stressed membranes with phononic crystal pattern
Electro-optomechanical equivalent circuits for quantum transduction
Using the techniques of optomechanics, a high- mechanical oscillator may
serve as a link between electromagnetic modes of vastly different frequencies.
This approach has successfully been exploited for the frequency conversion of
classical signals and has the potential of performing quantum state transfer
between superconducting circuitry and a traveling optical signal. Such
transducers are often operated in a linear regime, where the hybrid system can
be described using linear response theory based on the Heisenberg-Langevin
equations. While mathematically straightforward to solve, this approach yields
little intuition about the dynamics of the hybrid system to aid the
optimization of the transducer. As an analysis and design tool for such
electro-optomechanical transducers, we introduce an equivalent circuit
formalism, where the entire transducer is represented by an electrical circuit.
Thereby we integrate the transduction functionality of optomechanical systems
into the toolbox of electrical engineering allowing the use of its
well-established design techniques. This unifying impedance description can be
applied both for static (DC) and harmonically varying (AC) drive fields,
accommodates arbitrary linear circuits, and is not restricted to the
resolved-sideband regime. Furthermore, by establishing the quantized
input-output formalism for the equivalent circuit, we obtain the scattering
matrix for linear transducers using circuit analysis, and thereby have a
complete quantum mechanical characterization of the transducer. Hence, this
mapping of the entire transducer to the language of electrical engineering both
sheds light on how the transducer performs and can at the same time be used to
optimize its performance by aiding the design of a suitable electrical circuit.Comment: 30 pages, 9 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
Electromechanically induced absorption in a circuit nano-electromechanical system
A detailed analysis of electromechanically induced absorption (EMIA) in a
circuit nano-electromechanical hybrid system consisting of a superconducting
microwave resonator coupled to a nanomechanical beam is presented. By
performing two-tone spectroscopy experiments we have studied EMIA as a function
of the drive power over a wide range of drive and probe tone detunings. We find
good quantitative agreement between experiment and theoretical modeling based
on the Hamiltonian formulation of a generic electromechanical system. We show
that the absorption of microwave signals in an extremely narrow frequency band
(\Delta\omega/2\pi <5 Hz) around the cavity resonance of about 6 GHz can be
adjusted over a range of more than 25 dB on varying the drive tone power by a
factor of two. Possible applications of this phenomenon include notch filters
to cut out extremely narrow frequency bands (< Hz) of a much broader band of
the order of MHz defined by the resonance width of the microwave cavity. The
amount of absorption as well as the filtered frequency is tunable over the full
width of the microwave resonance by adjusting the power and frequency of the
drive field. At high drive power we observe parametric microwave amplification
with the nanomechanical resonator. Due to the very low loss rate of the
nanomechanical beam the drive power range for parametric amplification is
narrow, since the beam rapidly starts to perform self-oscillations.Comment: 16 pages, 5 figure
Multimode optomechanical system in the quantum regime
We realise a simple and robust optomechanical system with a multitude of
long-lived () mechanical modes in a phononic-bandgap shielded membrane
resonator. An optical mode of a compact Fabry-Perot resonator detects these
modes' motion with a measurement rate () that exceeds the
mechanical decoherence rates already at moderate cryogenic temperatures
(). Reaching this quantum regime entails, i.~a., quantum
measurement backaction exceeding thermal forces, and thus detectable
optomechanical quantum correlations. In particular, we observe ponderomotive
squeezing of the output light mediated by a multitude of mechanical resonator
modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for
detection losses) and bandwidths . The multi-mode
nature of the employed membrane and Fabry-Perot resonators lends itself to
hybrid entanglement schemes involving multiple electromagnetic, mechanical, and
spin degrees of freedom.Comment: 19 pages, 9 figure
Determination of effective mechanical properties of a double-layer beam by means of a nano-electromechanical transducer
We investigate the mechanical properties of a doubly-clamped, double-layer
nanobeam embedded into an electromechanical system. The nanobeam consists of a
highly pre-stressed silicon nitride and a superconducting niobium layer. By
measuring the mechanical displacement spectral density both in the linear and
the nonlinear Duffing regime, we determine the pre-stress and the effective
Young's modulus of the nanobeam. An analytical double-layer model
quantitatively corroborates the measured values. This suggests that this model
can be used to design mechanical multilayer systems for electro- and
optomechanical devices, including materials controllable by external parameters
such as piezoelectric, magnetrostrictive, or in more general multiferroic
materials.Comment: 4 pages, 4 figures, 1 supplemental materia
Mid-infrared frequency combs
Laser frequency combs are coherent light sources that emit a broad spectrum
consisting of discrete, evenly spaced narrow lines, each having an absolute
frequency measurable within the accuracy of an atomic clock. Their development,
a decade ago, in the near-infrared and visible domains has revolutionized
frequency metrology with numerous windfalls into other fields such as astronomy
or attosecond science. Extension of frequency comb techniques to the
mid-infrared spectral region is now under exploration. Versatile mid-infrared
frequency comb generators, based on novel laser gain media, nonlinear frequency
conversion or microresonators, promise to significantly expand the tree of
applications of frequency combs. In particular, novel approaches to molecular
spectroscopy in the fingerprint region, with dramatically improved precision,
sensitivity, recording time and/or spectral bandwidth may spark off new
discoveries in the various fields relevant to molecular sciences
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