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Observation of non-Markovian micromechanical Brownian motion.

Gröblacher S, Trubarov A, Prigge N, Cole GD, Aspelmeyer M, Eisert J - Nat Commun (2015)

Bottom Line: The precise decoherence mechanisms, however, are often unknown for a given system.In sharp contrast to what is commonly assumed in high-temperature quantum Brownian motion describing the dynamics of the mechanical degree of freedom, based on a statistical analysis of the emitted light, it is shown that this spectral density is highly non-Ohmic, reflected by non-Markovian dynamics, which we quantify.We conclude by elaborating on further applications of opto-mechanical systems in open system identification.

View Article: PubMed Central - PubMed

Affiliation: 1] Kavli Institute of Nanoscience, Delft University of Technology, Delft 2628 CJ, The Netherlands [2] Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna A-1090, Austria.

ABSTRACT
All physical systems are to some extent open and interacting with their environment. This insight, basic as it may seem, gives rise to the necessity of protecting quantum systems from decoherence in quantum technologies and is at the heart of the emergence of classical properties in quantum physics. The precise decoherence mechanisms, however, are often unknown for a given system. In this work, we make use of an opto-mechanical resonator to obtain key information about spectral densities of its condensed-matter heat bath. In sharp contrast to what is commonly assumed in high-temperature quantum Brownian motion describing the dynamics of the mechanical degree of freedom, based on a statistical analysis of the emitted light, it is shown that this spectral density is highly non-Ohmic, reflected by non-Markovian dynamics, which we quantify. We conclude by elaborating on further applications of opto-mechanical systems in open system identification.

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Sketch of the experiment.(a) The experimental set-up consists of a 1,064-nm Nd:YAG laser, which is split into a signal beam and a local oscillator (LO). The signal is phase-modulated with an electro-optical modulator (EOM) for Pound–Drever–Hall locking of the opto-mechanical cavity. In order to readout the phase of the signal beam acquired from the motion of the mechanical resonator, it is beaten with a strong LO on a beamsplitter and detected on two photodiodes. The phase φ between the LO and the signal is stabilized with the help of a mirror mounted on a piezo-ceramic actuator in order to only detect the phase quadrature of the signal field. The opto-mechanical cavity is kept at a pressure of <10−3 mbar to avoid residual-gas damping of the mechanical motion. (b) Scanning electron microscope picture of the tested device.
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f1: Sketch of the experiment.(a) The experimental set-up consists of a 1,064-nm Nd:YAG laser, which is split into a signal beam and a local oscillator (LO). The signal is phase-modulated with an electro-optical modulator (EOM) for Pound–Drever–Hall locking of the opto-mechanical cavity. In order to readout the phase of the signal beam acquired from the motion of the mechanical resonator, it is beaten with a strong LO on a beamsplitter and detected on two photodiodes. The phase φ between the LO and the signal is stabilized with the help of a mirror mounted on a piezo-ceramic actuator in order to only detect the phase quadrature of the signal field. The opto-mechanical cavity is kept at a pressure of <10−3 mbar to avoid residual-gas damping of the mechanical motion. (b) Scanning electron microscope picture of the tested device.

Mentions: We demonstrate our analysis on a micromechanical resonator as shown in Fig. 1b. The device consists of a 1-μm-thick layer of Si3N4 and is 150 μm long and 50 μm wide. The 50-μm diameter, high-reflectivity (R>99.991%) mirror pad in its centre allows to use this resonator as a mechanically moving end mirror in a Fabry–Pérot cavity, as has been fabricated to explore the regime of cavity opto-mechanical coupling3536 (for details on the fabrication process see ref. 37). In our case, the cavity finesse is intentionally kept low at F=2,300 by choosing a high-transmittivity input mirror for this experiment. This results in an amplitude cavity decay rate of κ=1.3 MHz (cavity length: 25 mm). By using a signal beam of 100 μW, we realize a sufficiently weak opto-mechanical coupling g≈40 kHz<<κ, such that the cavity field phase quadrature adiabatically follows the mechanical motion and hence δYout is a reliable measure of q. The fundamental mechanical resonance frequency is Ω=2π × 914 kHz, with a mechanical quality Q-factor of ∼215 at room temperature. Optical homodyne detection of the outgoing cavity field finally yields the temporal phase quadrature fluctuations δYout(t), which are digitized to calculate the noise power spectrum SδYout(ω) (see Fig. 1a). All experiments have been performed in vacuum (background pressure <10−3 mbar) to prevent the influence of fluidic damping. At the mentioned parameters for our experiment, we achieve a displacement sensitivity of ∼ as is shown in Fig. 2. To exclude the possible influence of spurious background noise we have also characterized the noise power spectrum of the cavity field without a mechanical resonator. In our configuration this is possible because of the specific design of the chip comprising the micromechanical device, which holds several non-suspended mirror pads that can be accessed by translating the chip. The resulting noise power spectrum is flat and hence cavity noise cannot contribute to any non-Brownian spectral signal (see Fig. 2). Another possible spectral dependence could arise from the presence of higher-order mechanical modes, which are not taken into account in equation 4. A finite element analysis of our mechanical system reveals the next mechanical mode at Ω(1)=2π × 1.2 MHz. As can be seen from Fig. 2, the spectral overlap in the vicinity of Ω is many orders of magnitude below the measured signal and hence negligible.


Observation of non-Markovian micromechanical Brownian motion.

Gröblacher S, Trubarov A, Prigge N, Cole GD, Aspelmeyer M, Eisert J - Nat Commun (2015)

Sketch of the experiment.(a) The experimental set-up consists of a 1,064-nm Nd:YAG laser, which is split into a signal beam and a local oscillator (LO). The signal is phase-modulated with an electro-optical modulator (EOM) for Pound–Drever–Hall locking of the opto-mechanical cavity. In order to readout the phase of the signal beam acquired from the motion of the mechanical resonator, it is beaten with a strong LO on a beamsplitter and detected on two photodiodes. The phase φ between the LO and the signal is stabilized with the help of a mirror mounted on a piezo-ceramic actuator in order to only detect the phase quadrature of the signal field. The opto-mechanical cavity is kept at a pressure of <10−3 mbar to avoid residual-gas damping of the mechanical motion. (b) Scanning electron microscope picture of the tested device.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4525213&req=5

f1: Sketch of the experiment.(a) The experimental set-up consists of a 1,064-nm Nd:YAG laser, which is split into a signal beam and a local oscillator (LO). The signal is phase-modulated with an electro-optical modulator (EOM) for Pound–Drever–Hall locking of the opto-mechanical cavity. In order to readout the phase of the signal beam acquired from the motion of the mechanical resonator, it is beaten with a strong LO on a beamsplitter and detected on two photodiodes. The phase φ between the LO and the signal is stabilized with the help of a mirror mounted on a piezo-ceramic actuator in order to only detect the phase quadrature of the signal field. The opto-mechanical cavity is kept at a pressure of <10−3 mbar to avoid residual-gas damping of the mechanical motion. (b) Scanning electron microscope picture of the tested device.
Mentions: We demonstrate our analysis on a micromechanical resonator as shown in Fig. 1b. The device consists of a 1-μm-thick layer of Si3N4 and is 150 μm long and 50 μm wide. The 50-μm diameter, high-reflectivity (R>99.991%) mirror pad in its centre allows to use this resonator as a mechanically moving end mirror in a Fabry–Pérot cavity, as has been fabricated to explore the regime of cavity opto-mechanical coupling3536 (for details on the fabrication process see ref. 37). In our case, the cavity finesse is intentionally kept low at F=2,300 by choosing a high-transmittivity input mirror for this experiment. This results in an amplitude cavity decay rate of κ=1.3 MHz (cavity length: 25 mm). By using a signal beam of 100 μW, we realize a sufficiently weak opto-mechanical coupling g≈40 kHz<<κ, such that the cavity field phase quadrature adiabatically follows the mechanical motion and hence δYout is a reliable measure of q. The fundamental mechanical resonance frequency is Ω=2π × 914 kHz, with a mechanical quality Q-factor of ∼215 at room temperature. Optical homodyne detection of the outgoing cavity field finally yields the temporal phase quadrature fluctuations δYout(t), which are digitized to calculate the noise power spectrum SδYout(ω) (see Fig. 1a). All experiments have been performed in vacuum (background pressure <10−3 mbar) to prevent the influence of fluidic damping. At the mentioned parameters for our experiment, we achieve a displacement sensitivity of ∼ as is shown in Fig. 2. To exclude the possible influence of spurious background noise we have also characterized the noise power spectrum of the cavity field without a mechanical resonator. In our configuration this is possible because of the specific design of the chip comprising the micromechanical device, which holds several non-suspended mirror pads that can be accessed by translating the chip. The resulting noise power spectrum is flat and hence cavity noise cannot contribute to any non-Brownian spectral signal (see Fig. 2). Another possible spectral dependence could arise from the presence of higher-order mechanical modes, which are not taken into account in equation 4. A finite element analysis of our mechanical system reveals the next mechanical mode at Ω(1)=2π × 1.2 MHz. As can be seen from Fig. 2, the spectral overlap in the vicinity of Ω is many orders of magnitude below the measured signal and hence negligible.

Bottom Line: The precise decoherence mechanisms, however, are often unknown for a given system.In sharp contrast to what is commonly assumed in high-temperature quantum Brownian motion describing the dynamics of the mechanical degree of freedom, based on a statistical analysis of the emitted light, it is shown that this spectral density is highly non-Ohmic, reflected by non-Markovian dynamics, which we quantify.We conclude by elaborating on further applications of opto-mechanical systems in open system identification.

View Article: PubMed Central - PubMed

Affiliation: 1] Kavli Institute of Nanoscience, Delft University of Technology, Delft 2628 CJ, The Netherlands [2] Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna A-1090, Austria.

ABSTRACT
All physical systems are to some extent open and interacting with their environment. This insight, basic as it may seem, gives rise to the necessity of protecting quantum systems from decoherence in quantum technologies and is at the heart of the emergence of classical properties in quantum physics. The precise decoherence mechanisms, however, are often unknown for a given system. In this work, we make use of an opto-mechanical resonator to obtain key information about spectral densities of its condensed-matter heat bath. In sharp contrast to what is commonly assumed in high-temperature quantum Brownian motion describing the dynamics of the mechanical degree of freedom, based on a statistical analysis of the emitted light, it is shown that this spectral density is highly non-Ohmic, reflected by non-Markovian dynamics, which we quantify. We conclude by elaborating on further applications of opto-mechanical systems in open system identification.

No MeSH data available.


Related in: MedlinePlus