Dephasing by electron-electron interactions in a ballistic Mach-Zehnder interferometer
Clemens Neuenhahn,
Florian Marquardt
New Journal of Physics
10
115018
(2008)
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We consider a ballistic Mach-Zehnder interferometer for electrons propagating chirally in one dimension (such as in an integer quantum Hall effect edge channel). In such a system, dephasing occurs when the finite range of the interaction potential is taken into account. Using the tools of bosonization, we discuss the decay of coherence as a function of propagation distance and energy. We supplement the exact solution by a semiclassical approach that is physically transparent and is exact at high energies. In particular, we study in more detail the recently predicted universal power-law decay of the coherence at high energies, where the exponent does not depend on the interaction strength. In addition, we compare against Keldysh perturbation theory, which works well for small interaction strength at short propagation distances.
Decoherence by quantum telegraph noise: A numerical evaluation
Benjamin Abel,
Florian Marquardt
Physical Review B
78
(20)
201302
(2008)
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We investigate the time evolution of a charge qubit subject to quantum telegraph noise produced by a single electronic defect level. We obtain results for the time evolution of the coherence that are strikingly different from the usual case of a harmonic-oscillator bath (Gaussian noise). When the coupling strength crosses a certain temperature-dependent threshold, we observe coherence oscillations in the strong-coupling regime. Moreover, we present the time evolution of the echo signal in a spin-echo experiment. Our analysis relies on a numerical evaluation of the exact solution for the density matrix of the qubit.
Dispersive optomechanics: a membrane inside a cavity
A. M. Jayich,
J. C. Sankey,
B. M. Zwickl,
C. Yang,
J. D. Thompson,
S. M. Girvin,
A. A. Clerk,
F. Marquardt,
J. G. E. Harris
New Journal of Physics
10
095008
(2008)
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We present the results of theoretical and experimental studies of dispersively coupled (or 'membrane in the middle') optomechanical systems. We calculate the linear optical properties of a high finesse cavity containing a thin dielectric membrane. We focus on the cavity's transmission, reflection and finesse as a function of the membrane's position along the cavity axis and as a function of its optical loss. We compare these calculations with measurements and find excellent agreement in cavities with empty-cavity finesses in the range 10(4)-10(5). The imaginary part of the membrane's index of refraction is found to be similar to 10(-4). We calculate the laser cooling performance of this system, with a particular focus on the less-intuitive regime in which photons 'tunnel' through the membrane on a timescale comparable to the membrane's period of oscillation. Lastly, we present calculations of quantum non-demolition measurements of the membrane's phonon number in the low signal-to-noise regime where the phonon lifetime is comparable to the QND readout time.
The optomechanical instability in the quantum regime
Max Ludwig,
Bjoern Kubala,
Florian Marquardt
New Journal of Physics
10
095013
(2008)
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We consider a generic optomechanical system, consisting of a driven optical cavity and a movable mirror attached to a cantilever. Systems of this kind (and analogues) have been realized in many recent experiments. It is well known that these systems can exhibit an instability towards a regime where the cantilever settles into self-sustained oscillations. In this paper, we briefly review the classical theory of the optomechanical instability, and then discuss the features arising in the quantum regime. We solve numerically a full quantum master equation for the coupled system, and use it to analyze the photon number, the cantilever's mechanical energy, the phonon probability distribution and the mechanical Wigner density, as a function of experimentally accessible control parameters. When a suitable dimensionless 'quantum parameter' is sent to zero, the results of the quantum mechanical model converge towards the classical predictions. We discuss this quantum-to-classical transition in some detail.
Back-action evasion and squeezing of a mechanical resonator using a cavity detector
A. A. Clerk,
F. Marquardt,
K. Jacobs
New Journal of Physics
10
095010
(2008)
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We study the quantum measurement of a cantilever using a parametrically coupled electromagnetic cavity which is driven at the two sidebands corresponding to the mechanical motion. This scheme, originally due to Braginsky et al (Braginsky V, Vorontsov Y I and Thorne K P 1980 Science 209 547), allows a back-action free measurement of one quadrature of the cantilever's motion, and hence the possibility of generating a squeezed state. We present a complete quantum theory of this system, and derive simple conditions on when the quantum limit on the added noise can be surpassed. We also study the conditional dynamics of the measurement, and discuss how such a scheme (when coupled with feedback) can be used to generate and detect squeezed states of the oscillator. Our results are relevant to experiments in optomechanics, and to experiments in quantum electromechanics employing stripline resonators coupled to mechanical resonators.
Self-induced oscillations in an optomechanical system driven by bolometric backaction
Constanze Metzger,
Max Ludwig,
Clemens Neuenhahn,
Alexander Ortlieb,
Ivan Favero,
Khaled Karrai,
Florian Marquardt
We have explored the nonlinear dynamics of an optomechanical system consisting of an illuminated Fabry-Perot cavity, one of whose end mirrors is attached to a vibrating cantilever. The backaction induced by the bolometric light force produces negative damping such that the system enters a regime of nonlinear oscillations. We study the ensuing attractor diagram describing the nonlinear dynamics. A theory is presented that yields quantitative agreement with experimental results. This includes the observation of a regime where two mechanical modes of the cantilever are excited simultaneously.
Measuring the size of a quantum superposition of many-body states
Florian Marquardt,
Benjamin Abel,
Jan von Delft
Physical Review A
78
(1)
012109
(2008)
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We propose a measure for the "size" of a quantum superposition of two many-body states with (supposedly) macroscopically distinct properties by counting how many single-particle operations are needed to map one state onto the other. This definition gives sensible results for simple, analytically tractable cases and is consistent with a previous definition restricted to Greenberger-Horne-Zeilinger-like states. We apply our measure to the experimentally relevant, nontrivial example of a superconducting three-junction flux qubit put into a superposition of left- and right-circulating supercurrent states, and we find the size of this superposition to be surprisingly small.
Optomechanical set-ups use radiation pressure to manipulate macroscopic mechanical objects. Two experiments transfer this concept to the fields of superconducting microwave circuits and cold-atom physics.
Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane (vol 452, pg 72, 2008)
J. D. Thompson,
B. M. Zwickl,
A. M. Jayich,
Florian Marquardt,
S. M. Girvin,
J. G. E. Harris
Macroscopic mechanical objects and electromagnetic degrees of freedom can couple to each other through radiation pressure. Optomechanical systems in which this coupling is sufficiently strong are predicted to show quantum effects and are a topic of considerable interest. Devices in this regime would offer new types of control over the quantum state of both light and matter(1-4), and would provide a new arena in which to explore the boundary between quantum and classical physics(5-7). Experiments so far have achieved sufficient optomechanical coupling to laser- cool mechanical devices(8-12), but have not yet reached the quantum regime. The outstanding technical challenge in this field is integrating sensitive micromechanical elements ( which must be small, light and flexible) into high- finesse cavities ( which are typically rigid and massive) without compromising the mechanical or optical properties of either. A second, and more fundamental, challenge is to read out the mechanical element's energy eigenstate. Displacement measurements ( no matter how sensitive) cannot determine an oscillator's energy eigenstate(13), and measurements coupling to quantities other than displacement(14-16) have been difficult to realize in practice. Here we present an optomechanical system that has the potential to resolve both of these challenges. We demonstrate a cavity which is detuned by the motion of a 50-nm- thick dielectric membrane placed between two macroscopic, rigid, high- finesse mirrors. This approach segregates optical and mechanical functionality to physically distinct structures and avoids compromising either. It also allows for direct measurement of the square of the membrane's displacement, and thus in principle the membrane's energy eigenstate. We estimate that it should be practical to use this scheme to observe quantum jumps of a mechanical system, an important goal in the field of quantum measurement.
Kontakt
Theorie-Abteilung Prof. Florian Marquardt
Max-Planck-Institut für die Physik des Lichts Staudtstr. 2 91058 Erlangen
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