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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 9 — May. 6, 2013
  • pp: 11227–11236
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Optical coupling to nanoscale optomechanical cavities for near quantum-limited motion transduction

Justin D. Cohen, Seán M. Meenehan, and Oskar Painter  »View Author Affiliations


Optics Express, Vol. 21, Issue 9, pp. 11227-11236 (2013)
http://dx.doi.org/10.1364/OE.21.011227


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Abstract

A significant challenge in the development of chip-scale cavity-optomechanical devices as testbeds for quantum experiments and classical metrology lies in the coupling of light from nanoscale optical mode volumes to conventional optical components such as lenses and fibers. In this work we demonstrate a high-efficiency, single-sided fiber-optic coupling platform for optomechanical cavities. By utilizing an adiabatic waveguide taper to transform a single optical mode between a photonic crystal zipper cavity and a permanently mounted fiber, we achieve a collection efficiency for intracavity photons of 52% at the cavity resonance wavelength of λ ≈ 1538 nm. An optical balanced homodyne measurement of the displacement fluctuations of the fundamental in-plane mechanical resonance at 3.3 MHz reveals that the imprecision noise floor lies a factor of 2.8 above the standard quantum limit (SQL) for continuous position measurement, with a predicted total added noise of 1.4 phonons at the optimal probe power. The combination of extremely low measurement noise and robust fiber alignment presents significant progress towards single-phonon sensitivity for these sorts of integrated micro-optomechanical cavities.

© 2013 OSA

1. Introduction

Nanoscale structures in the form of photonic and phononic crystals have recently been shown to feature significant radiation pressure interactions between localized optical cavity modes and internal nanomechanical resonances [1

1. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009) [CrossRef] [PubMed] .

]. Alongside similar advances in the microwave domain [2

2. J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Siroi, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011) [CrossRef] [PubMed] .

], optomechanical crystals have recently been used to laser cool a nanomechanical oscillator to its quantum ground state [3

3. J. Chan, T. Mayer-Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011) [CrossRef] [PubMed] .

]. The ability to measure and control the quantum state of such an object ultimately hinges on the quantum efficiency of the optical transduction of motion. Here we demonstrate high-efficiency optical coupling between an optomechanical zipper cavity [4

4. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. J. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550–555 (2009) [CrossRef] [PubMed] .

] and a permanently mounted optical fiber through adiabatic mode conversion. This optical coupling technique greatly improves the collection efficiency of light from these types of optomechanical cavities over existing methods, and brings the minimum total added measurement noise to within a factor of 3 of the standard-quantum-limit of continuous position measurement.

In a weak measurement of position through a parametrically coupled optical cavity there are two intrinsic sources of measurement noise. Shot noise of the probe laser and excess quantum vacuum noise due to optical signal loss set the fundamental noise floor of the measurement. When converted into units of mechanical quanta this imprecision noise Nimp decreases with increasing probe power. However, higher laser probe power comes at the cost of radiation pressure backaction driving an additional occupation noise NBA on top of the thermal mode occupation Nth. For an optically resonant measurement of position, the noise terms in units of mechanical occupation quanta are
Nimp=κ2γ64ncg2κeηcplηmeas,NBA=4ncg2κγ,
(1)
where g is the optomechanical interaction rate, κ and γ are respectively the optical and mechanical loss rates, κe is the extrinsic cavity loss rate, ηcpl is the optical efficiency between the cavity and the detection channel, and ηmeas accounts for excess technical noise and signal loss accumulated in experiment-specific optical components. As intracavity photon number nc is varied, an optimal input power Pmin is reached where the imprecision noise and back-action noises are equal and the total added noise is minimized to
Nmin=(Nimp+NBA)min=12ηcplηmeasκe/κ.
(2)

In the ideal case this point, known as the standard-quantum-limit (SQL), adds 1/2 quanta of noise to the measurement, equal to the zero-point fluctuations of the oscillator [5

5. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement and amplification,” Rev. Mod. Phys. 82, 1155–1208 (2010) [CrossRef] .

]. The SQL can only be reached in the limit of noise-free, lossless detection (ηcplηmeas = 1) and perfect waveguide loading (κe = κ). Thus, Nmin is a suitable figure of merit for the ultimate quantum efficiency of an optomechanical detector of position. Although experiments in both the optical and microwave domains have brought the imprecision noise level down to below 1/4 quanta [6

6. J. Teufel, T. Donner, M. Castellanos-Beltran, J. Harlow, and K. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nature Nanotech. 4, 820–823 (2009) [CrossRef] .

, 7

7. G. Anetsberger, E. Gavartin, O. Arcizet, Q. Unterreithmeier, E. Weig, M. Gorodetsky, J. Kotthaus, and T. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010) [CrossRef] .

], and recent microwave experiments have achieved total added noise within a factor of 4 of the SQL [2

2. J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Siroi, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011) [CrossRef] [PubMed] .

], current state-of-the-art optical devices have been limited to 14 – 80 times the SQL [3

3. J. Chan, T. Mayer-Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011) [CrossRef] [PubMed] .

, 8

8. R. Rivière, S. Deléglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83, 063835 (2011) [CrossRef] .

, 9

9. S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nature Phys. 5, 485–488 (2009) [CrossRef] .

]. Such experiments are limited partly by technical noise (e.g. added noise from amplifiers), but a substantial amount of imprecision is introduced by poor quantum efficiency of the optical readout. Here we identify another figure of merit to allow for cross-platform comparison of detection methods. The quantum efficiency of a general measurement apparatus will be limited to ηCE = ηcplκe/κ, the collection efficiency of intracavity photons into the detection channel before further signal processing.

To date, most nanoscale optomechanical experiments utilize evanescent coupling between the optical cavity and an adiabatically tapered optical fiber [10

10. C. Michael, M. Borselli, T. Johnson, C. Chrystal, and O. Painter, “An optical fiber-taper probe for wafer-scale microphotonic device characterization,” Opt. Express 15, 4745–4752 (2007) [CrossRef] [PubMed] .

, 11

11. S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003) [CrossRef] [PubMed] .

]. While this method offers low parasitic losses, standing wave resonators such as the optomechanical cavities considered here radiate symmetrically into two oppositely propagating modes of the fiber, each at a rate κe. Thus the fraction of nc routed into the detection channel κe/κ = κe/(κi + 2κe) does not exceed 1/2 even in the ideal case of negligible intrinsic cavity loss rate κi. To reach the overcoupled regime κe/κ > 1/2, a single-sided coupling scheme is necessary.

2. Single-sided fiber coupling

We have implemented a coupling scheme which routes light from a photonic crystal zipper cavity to a cleaved single-mode optical fiber tip with high efficiency in a fully single-sided interface. The fiber is self-aligned in a Si V-groove (Fig. 1), secured with epoxy, and butt-coupled to a mode-matched Si3N4 waveguide, which adiabatically widens [12

12. O. Mitomi, K. Kasaya, and H. Miyazawa, “Design of a single-mode tapered waveguide for low-loss chip-to-fiber coupling,” IEEE J. Quantum Electron. 30, 1787–1793 (1994) [CrossRef] .

15

15. L. Chen, C. R. Doerr, Y.-K. Chen, and T.-Y. Liow, “Low-loss and broadband cantilever couplers between standard cleaved fibers and high-index-contrast Si3N4 or Si waveguides,” IEEE Photon. Technol. Lett. 22, 1744–1746 (2010) [CrossRef] .

] to match the width of the zipper cavity nanobeam. The waveguide then end-couples to the cavity through a truncated photonic crystal mirror. The robust fiber alignment offers another key advantage over evanescent and grating-coupler techniques that call for nanometer-scale-sensitive positioning to achieve appreciable mode overlap. Nano-positioning is difficult and expensive to implement in cryogenic setups due to footprint and imaging requirements, whereas the coupler presented here can be installed directly into any system with a fiber port. While the reported coupling method is particularly useful for attaining single-sided coupling to photonic crystal cavities, it could also be adapted to traveling wave resonators by employing a side-coupled geometry in an on-chip analogue to fiber-taper probing.

Fig. 1 Scanning electron microscope (SEM) images illustrating the optical coupling scheme and mode conversion junctions, with overlayed mode profiles simulated via Finite-Element-Method (FEM) of optical power in (c) and (d), and electric field in (e) and (f). (a) Fabricated device after fiber coupling via self-aligned v-groove placement. (b) Detailed view of the zipper cavity. (c) The optical-fiber/Si3N4-waveguide junction. (d) The waveguide with supporting tethers after adiabatically widening to 1.5 μm. (e) Photonic crystal taper section. (f) Photonic crystal defect cavity.

We now describe the optimization of the optical efficiency. To determine the optimal width of the Si3N4 waveguide, we compute the guided transverse modes of both the waveguide and the optical fiber at the target wavelength of λ = 1550 nm using a finite-element-method (FEM) solver [16

16. COMSOL Multiphysics http://www.comsol.com/.

]. The coupling efficiency at the fiber-waveguide junction is calculated from the mode profiles using a mode overlap integral [17

17. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Springer, 1983).

]. For a 400 nm thick Si3N4 membrane, the optimal waveguide width is w = 230 nm with a transmission efficiency of ηoverlap = 95% as depicted in Fig. 1(c). Then w increases gradually to the nanobeam width of 850 nm. To obtain high transmission efficiency in this tapered waveguide section, the rate of change of w along the propagation direction z must be small enough to satisfy the adiabatic condition [17

17. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Springer, 1983).

]dw/dz ≪ Δneff at every point along the taper, where Δneff is the difference in effective index between the fundamental waveguide mode and any other guided or radiation mode. The actual transmission efficiency is calculated using a finite-difference-time-domain (FDTD) simulation [18

18. Lumerical Solutions Inc., http://www.lumerical.com/tcad-products/fdtd/.

]. For a 400 μm long taper with a cubic shape between the junctions shown in Figs. 1(c,d), we obtain a transmission efficiency of ηtaper = 98%.

The high-stress Si3N4 film used here, desirable for its excellent optical and mechanical quality, deforms out of plane significantly when suspended over lengths greater than 10 – 20 μm. For this reason a 70 nm wide tether is placed near the fiber-waveguide junction (Fig. 1(c)) to fix the waveguide taper in position for optimal fiber alignment [19

19. Potentially, the use of a lensed or small-mode-field-diameter fiber could allow for a larger initial waveguide width, correspondingly shorter tapering region, and the ability to eliminate the support tether. However such an approach would be less robust to slight fiber misalignments arising from fabrication variability of the V-groove size on the order of 100 – 200 nm. These misalignments are small relative to the 10 μm mode diameter used in the reported device, but would cause substantial mode-mismatch in any scheme with a short waveguide taper. The optimal mode-matching of the junction would also likely be diminished, as increased mode confinement in the waveguide tip would render the profile less circularly symmetric.

]. The scattering loss of the tether is computed using FDTD and the transmission efficiency is calculated to be ηtether = 95%. A second set of 150 nm wide tethers (Fig. 1(d)) is placed just before the cavity, in order to isolate the optomechanical crystal from the low-frequency vibrational modes of the tapered waveguide. The waveguide is temporarily widened to 1.5 μm at this point, rendering the scattering loss due to the tethers negligible.

Finally, the uniform dielectric waveguide adiabatically transitions into a one-dimensional photonic crystal mirror by linearly increasing the radius of the holes while keeping the lattice constant fixed. An 8 hole photonic crystal taper (Fig. 1(e)) is sufficient to achieve an efficiency of ηmirror = 95%. The coupling rate to the cavity is controlled by varying the number of mirror periods after the taper. The photonic crystal cavity mode (Fig. 1(f)) is shared between the waveguide beam and a near-field, flexibly supported test beam, with the optomechanical coupling arising from the sensitivity of the resonance frequency to the beam separation. In this manner the waveguide structure serves as an optical readout of the test beam motion with an optimal round-trip efficiency of ηrt = (ηoverlapηtaperηtether)2ηmirror = 74%. For the purposes of optomechanical transduction, the relevant figure is the single-pass transmission efficiency between the cavity output and the fiber, which ideally is ηcpl=ηrt=86%.

3. Optical characterization

Fig. 2 Optical response of the system. (a) A wide range reflection scan reveals Fabry-Perot interference fringes off-resonant from the photonic crystal cavity, and sharp dips on resonance. The visibility of the fringes reveals that ηcpl has the wavelength dependence shown in solid green in (b), with ηcpl = 74.6 % at the cavity resonance wavelength of λ ≈ 1538 nm. The dashed green line denotes the simulated ideal efficiency of the coupler. (c) By tuning the number of mirror-type-hole periods between the coupling section and cavity section of the photonic crystal, the total quality factor Qt (green points) of the resonance transitions from being limited by intrinsic loss Qi (blue points) to extrinsic loss Qe (red points) in good agreement with simulation (dashed red curve). (d) The ratio of extrinsic loss rate κe to total loss rate κ progresses from the strongly undercoupled regime to the strongly overcoupled regime with the mirror variation.

4. Mechanical spectroscopy

To extract the noise power spectral density (NPSD) of the test-beam displacement Sxx from the optomechanically phase-shifted cavity reflection, we place the device in an evacuated environment and connect the output fiber to the signal arm of a fiber-based balanced homodyne receiver shown schematically in Fig. 3. We resonantly probe the optical mode to avoid dynamic back-action on the test beam as well as to maximize the mechanical transduction sensitivity. The probe laser frequency is positioned on resonance without frequency-locking to the cavity as drift is found to be negligible over the time span of the measurement (∼ 100 s). The laser output is sent through a fiber polarization controller (FPC) and variable optical attenuator (VOA) before being split by a variable beam splitter (VBS1) into into the signal and local oscillator (LO) arms of the homodyne receiver. The signal circulates through the device, while the LO propagates through a fiber stretcher (FS) before recombining with the signal at VBS2, with the interference output detected on a balanced photodiode (BPD) pair. The difference signal generated by the BPD is dediplexed at 200 kHz into a low-frequency lock signal (fed back through a proportional-integral-derivative (PID) controller onto the FS to eliminate path-length fluctuations in the interferometer) and a high-frequency photocurrent response. The NPSD of this high-frequency signal, SII(ω), is measured on an electronic spectrum analyzer (ESA) and plotted in Fig. 4 for a probe power of 10 nW. The optical efficiency of the setup to the device reflection signal is set by the transmission through the circulator (87 %) and VBS2 (94 %) as well as the BPD quantum efficiency (44 %), which combine to ηmeas = 36%.

Fig. 3 Experimental setup. FPC: fiber polarization controller. VOA: variable optical attenuator. VBS: variable beam splitter. LO: local oscillator. DUT: device under test. FS: fiber stretcher. PID: proportional-integral-derivative controller. BPD: balanced photodiode. ESA: electronic spectrum analyzer.
Fig. 4 Photocurrent NPSD SII(ω) (solid black curve) measured on the ESA with 10 nW of input signal arm power. Optical shot noise (solid blue curve) sets the noise floor several dBm above electronic noise contributions (solid orange curve.) The two peaks at 3.14 MHz and 3.3 MHz correspond to the first order mechanical bending modes of the waveguide and test beams respectively. The dashed red and green curves display the calculated single-sided displacement NPSD of each mode, with the calculated imprecision noise floor shown in the dashed purple line. (insets) FEM simulated mechanical bending modes of each beam.

The NPSD shown in Fig. 4 reveals a prominent resonance at ω = 3.3 MHz, which is identified using FEM simulations as the fundamental in-plane mechanical mode of the test beam. The optomechanical coupling rate of this mode, calibrated through the optical spring shift [4

4. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. J. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550–555 (2009) [CrossRef] [PubMed] .

], is g/2π = 350 kHz. A second prominent resonance exists at ω = 3.15 MHz which is identified as the fundamental in-plane mechanical mode of the waveguide with a lower optomechanical coupling (g/2π = 135 kHz) owing to small overlap between the mechanical and optical modes. Overlays of the predicted single-sided transduction spectra, calculated using the measured parameters of the optomechanical cavity and fiber coupler, show good agreement with the measured signal for both the test-beam (dashed green curve) and the waveguide (dashed red curve). Other peaks at 3 MHz, 3.2 MHz, and 3.4 MHz do not correspond to any real mechanical motion of the beam but rather are due to nonlinear transduction of the mechanics. Thermal Brownian motion of the beams, combined with the large optomechanical coupling, gives rise to a frequency shift of the optical mode which is a substantial fraction of the cavity optical linewidth, leading to harmonics in SII(ω) at multiples of the sum and difference frequencies of the two mechanical modes [20

20. Q. Lin, J. Rosenberg, X. Jiang, K. Vahala, and O. Painter, “Mechanical Oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 10360 (2009) [CrossRef] .

]. The remaining small features in SII(ω) are due to out-of-plane flexural modes of the structure, which are weakly transduced due to imperfect vertical symmetry.

5. Measurement imprecision and discussion

For the remainder of this work we focus our discussion on measurement of the mechanical mode with the strongest transduction, the fundamental in-plane mode of the test beam with mechanical frequency ωm = 3.3 MHz. The single-sided NPSD of displacement for a harmonic mechanical mode at the mechanical resonance frequency is given by Sxx(ωm)=8xZPF2(n+1/2)/γ, where xZPF=h¯/2mωm is the zero-point amplitude of the mechanical resonator with effective motional mass m, and 〈n〉 = Nth + NBA is the mode occupancy in units of phonon quanta. For the fundamental in-plane mode we numerically compute an effective mass of m = 15 pg and a corresponding zero-point amplitude of xZPF = 13 fm. When the mechanical mode is well-resolved in SII(ω), that is, when the contributions of nearby mechanical modes are negligible and the resolution bandwidth of the ESA is much less than γ/2π = 150 Hz, we can convert the spectrum into units of displacement for the measured mechanical mode by scaling SII(ωm) to the computed value of Sxx(ωm).

We determine the imprecision in units of quanta for a measurement of this mechanical mode by referencing the measured background level to the height of the measured noise peak. That is, the number of imprecision quanta is equal to (〈n〉+1/2) divided by the signal-to-noise ratio (SNR) of the resolved mechanical noise peak to the imprecision noise floor, so that an imprecision level of Nimp = 1 corresponds to the equivalent level of NPSD that would be produced at the mechanical mode noise peak by a single quantum in the mechanical resonator [3

3. J. Chan, T. Mayer-Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011) [CrossRef] [PubMed] .

]. To determine the background noise floor we take the average of SII(ω) from 2.4 – 2.6 MHz, indicated by relatively noise-free spectral region shaded gray in Fig. 5(a).

Fig. 5 (a) Signal-to-noise ratio (SNR) of SII(ω) measured with 880 pW (magenta), 8.6 nW (cyan), and 76 nW (orange) probe power from which the imprecision point of corresponding color is extracted in (b). The dashed peak levels are referenced to the background level indicated by the gray shaded region. (b) Noise quanta versus probe power. Measurements of imprecision are plotted with calculated imprecision (blue), estimated back-action (red), and total (green) noise quanta are plotted in solid curves for the device under test and dashed curves for an ideal measurement.

To directly measure the additional phonon occupation due to back-action it is necessary to determine the total phonon occupancy, 〈n〉, by integrating over the full bandwidth of the mechanical mode. However, such a study is outside the scope of the work presented here, as the large thermal occupation at room temperature (Nth ≈ 106) dominates the signal over the comparatively small back-action, NBA, produced by reasonable laser probe powers. For now we restrict our attention to measuring the imprecision, and assume that the backaction is due only to the ideal radiation pressure term given in Eq. (1). This assumption is supported by measurements of the properties of known noise sources such as technical laser noise [21

21. While in principle both intensity and phase noise of the laser can contribute to the heating of the mechanical mode, for an optically resonant measurement of position in the sideband unresolved regime the phase noise does not contribute to backaction and only intensity noise affects the mechanics. In this regime the phase noise adds a small component to the imprecision noise floor. Measurements of the phase and intensity noise of our laser reveal no excess intensity noise and a flat frequency NPSD of Sωω= 5 × 103rad2Hz in the frequency range of interest. Consequently, for the probe powers used in this work, the excess back-action due to technical laser noise is negligible, and the phase noise contribution to the noise floor lies roughly 60 dB below the shot noise.

], which is a common concern in optomechanical systems [22

22. P. Rabl, C. Genes, K. Hammerer, and M. Aspelmeyer, “Phase-noise induced limitations on cooling and coherent evolution in optomechanical systems,” Phys. Rev. A 80, 063819 (2009) [CrossRef] .

24

24. A. M. Jayich, J. C. Sankey, K. Bjorke, D. Lee, C. Yang, M. Underwood, L. Childress, A. Petrenko, S. M. Girvin, and J. G. E. Harris, “Cryogenic optomechanics with a Si3N4 membrane and classical laser noise,” New J. Phys. 14, 115018 (2012) [CrossRef] .

]. As there may exist additional, unknown sources of excess back-action in our measurement, we emphasize that the main result of this work is the collection efficiency of the coupling scheme, and that back-action and noise-driven occupation levels are used only to compare the ideal quantum limits of the device to the SQL.

It is worth noting that improvements to ηmeas of the optical circuit such as higher efficiency photodiodes can lower Nmin to below 1 quantum. In addition to improving the collection efficiency towards the theoretical maximum of ηCE = 86%, further work will focus on measuring the back-action exerted on the resonator by placing the device in suitable cryogenic conditions where the thermal occupation is strongly suppressed. Another key application which benefits greatly from the improved collection efficiency demonstrated here is feedback damping of the mechanical motion [26

26. C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77, 033804 (2008) [CrossRef] .

,27

27. K. D. Bouwmeester and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 75–78 (2006) [CrossRef] [PubMed] .

], which is fundamentally limited by the imprecision noise and could enable ground state cooling of sideband unresolved mechanical systems such as the zipper cavity.

Acknowledgments

This work was supported by the DARPA/MTO ORCHID and MESO programs, the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation, and by the AFOSR QuMPASS MURI. We gratefully acknowledge critical support and infrastructure provided for this work by the Kavli Nanoscience Institute at Caltech.

References and links

1.

M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009) [CrossRef] [PubMed] .

2.

J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Siroi, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011) [CrossRef] [PubMed] .

3.

J. Chan, T. Mayer-Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011) [CrossRef] [PubMed] .

4.

M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. J. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature 459, 550–555 (2009) [CrossRef] [PubMed] .

5.

A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, “Introduction to quantum noise, measurement and amplification,” Rev. Mod. Phys. 82, 1155–1208 (2010) [CrossRef] .

6.

J. Teufel, T. Donner, M. Castellanos-Beltran, J. Harlow, and K. Lehnert, “Nanomechanical motion measured with an imprecision below that at the standard quantum limit,” Nature Nanotech. 4, 820–823 (2009) [CrossRef] .

7.

G. Anetsberger, E. Gavartin, O. Arcizet, Q. Unterreithmeier, E. Weig, M. Gorodetsky, J. Kotthaus, and T. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A 82, 061804 (2010) [CrossRef] .

8.

R. Rivière, S. Deléglise, S. Weis, E. Gavartin, O. Arcizet, A. Schliesser, and T. Kippenberg, “Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state,” Phys. Rev. A 83, 063835 (2011) [CrossRef] .

9.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nature Phys. 5, 485–488 (2009) [CrossRef] .

10.

C. Michael, M. Borselli, T. Johnson, C. Chrystal, and O. Painter, “An optical fiber-taper probe for wafer-scale microphotonic device characterization,” Opt. Express 15, 4745–4752 (2007) [CrossRef] [PubMed] .

11.

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003) [CrossRef] [PubMed] .

12.

O. Mitomi, K. Kasaya, and H. Miyazawa, “Design of a single-mode tapered waveguide for low-loss chip-to-fiber coupling,” IEEE J. Quantum Electron. 30, 1787–1793 (1994) [CrossRef] .

13.

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28, 1302–1304 (2003) [CrossRef] [PubMed] .

14.

S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguids,” Opt. Express 11, 2927–2939 (2003) [CrossRef] [PubMed] .

15.

L. Chen, C. R. Doerr, Y.-K. Chen, and T.-Y. Liow, “Low-loss and broadband cantilever couplers between standard cleaved fibers and high-index-contrast Si3N4 or Si waveguides,” IEEE Photon. Technol. Lett. 22, 1744–1746 (2010) [CrossRef] .

16.

COMSOL Multiphysics http://www.comsol.com/.

17.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Springer, 1983).

18.

Lumerical Solutions Inc., http://www.lumerical.com/tcad-products/fdtd/.

19.

Potentially, the use of a lensed or small-mode-field-diameter fiber could allow for a larger initial waveguide width, correspondingly shorter tapering region, and the ability to eliminate the support tether. However such an approach would be less robust to slight fiber misalignments arising from fabrication variability of the V-groove size on the order of 100 – 200 nm. These misalignments are small relative to the 10 μm mode diameter used in the reported device, but would cause substantial mode-mismatch in any scheme with a short waveguide taper. The optimal mode-matching of the junction would also likely be diminished, as increased mode confinement in the waveguide tip would render the profile less circularly symmetric.

20.

Q. Lin, J. Rosenberg, X. Jiang, K. Vahala, and O. Painter, “Mechanical Oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett. 103, 10360 (2009) [CrossRef] .

21.

While in principle both intensity and phase noise of the laser can contribute to the heating of the mechanical mode, for an optically resonant measurement of position in the sideband unresolved regime the phase noise does not contribute to backaction and only intensity noise affects the mechanics. In this regime the phase noise adds a small component to the imprecision noise floor. Measurements of the phase and intensity noise of our laser reveal no excess intensity noise and a flat frequency NPSD of Sωω= 5 × 103rad2Hz in the frequency range of interest. Consequently, for the probe powers used in this work, the excess back-action due to technical laser noise is negligible, and the phase noise contribution to the noise floor lies roughly 60 dB below the shot noise.

22.

P. Rabl, C. Genes, K. Hammerer, and M. Aspelmeyer, “Phase-noise induced limitations on cooling and coherent evolution in optomechanical systems,” Phys. Rev. A 80, 063819 (2009) [CrossRef] .

23.

A. H. Safavi-Naeini, J. Chan, J. T. Hill, S. Gröblacher, H. Miao, Y. Chen, M. Aspelmeyer, and O. Painter, “Laser noise in cavity-optomechanical cooling and thermometry,” New J. Phys. 15, 035007 (2013) [CrossRef] .

24.

A. M. Jayich, J. C. Sankey, K. Bjorke, D. Lee, C. Yang, M. Underwood, L. Childress, A. Petrenko, S. M. Girvin, and J. G. E. Harris, “Cryogenic optomechanics with a Si3N4 membrane and classical laser noise,” New J. Phys. 14, 115018 (2012) [CrossRef] .

25.

T. P. Purdy, R. W. Peterson, and C. A. Regal, “Observation of radiation pressure shot noise on a macroscopic object,” Science 339, 801–804 (2013) [CrossRef] [PubMed] .

26.

C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A 77, 033804 (2008) [CrossRef] .

27.

K. D. Bouwmeester and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature 444, 75–78 (2006) [CrossRef] [PubMed] .

OCIS Codes
(230.3120) Optical devices : Integrated optics devices
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(280.4788) Remote sensing and sensors : Optical sensing and sensors
(230.5298) Optical devices : Photonic crystals
(120.4880) Instrumentation, measurement, and metrology : Optomechanics

ToC Category:
Optical Devices

History
Original Manuscript: February 8, 2013
Revised Manuscript: April 22, 2013
Manuscript Accepted: April 22, 2013
Published: May 1, 2013

Citation
Justin D. Cohen, Seán M. Meenehan, and Oskar Painter, "Optical coupling to nanoscale optomechanical cavities for near quantum-limited motion transduction," Opt. Express 21, 11227-11236 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-11227


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References

  1. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature462, 78–82 (2009). [CrossRef] [PubMed]
  2. J. Teufel, T. Donner, D. Li, J. Harlow, M. Allman, K. Cicak, A. Siroi, J. Whittaker, K. Lehnert, and R. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature475, 359–363 (2011). [CrossRef] [PubMed]
  3. J. Chan, T. Mayer-Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature478, 89–92 (2011). [CrossRef] [PubMed]
  4. M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. J. Painter, “A picogram- and nanometre-scale photonic-crystal optomechanical cavity,” Nature459, 550–555 (2009). [CrossRef] [PubMed]
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  7. G. Anetsberger, E. Gavartin, O. Arcizet, Q. Unterreithmeier, E. Weig, M. Gorodetsky, J. Kotthaus, and T. Kippenberg, “Measuring nanomechanical motion with an imprecision below the standard quantum limit,” Phys. Rev. A82, 061804 (2010). [CrossRef]
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  9. S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, “Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity,” Nature Phys.5, 485–488 (2009). [CrossRef]
  10. C. Michael, M. Borselli, T. Johnson, C. Chrystal, and O. Painter, “An optical fiber-taper probe for wafer-scale microphotonic device characterization,” Opt. Express15, 4745–4752 (2007). [CrossRef] [PubMed]
  11. S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett.91, 043902 (2003). [CrossRef] [PubMed]
  12. O. Mitomi, K. Kasaya, and H. Miyazawa, “Design of a single-mode tapered waveguide for low-loss chip-to-fiber coupling,” IEEE J. Quantum Electron.30, 1787–1793 (1994). [CrossRef]
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  14. S. J. McNab, N. Moll, and Y. A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguids,” Opt. Express11, 2927–2939 (2003). [CrossRef] [PubMed]
  15. L. Chen, C. R. Doerr, Y.-K. Chen, and T.-Y. Liow, “Low-loss and broadband cantilever couplers between standard cleaved fibers and high-index-contrast Si3N4 or Si waveguides,” IEEE Photon. Technol. Lett.22, 1744–1746 (2010). [CrossRef]
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  19. Potentially, the use of a lensed or small-mode-field-diameter fiber could allow for a larger initial waveguide width, correspondingly shorter tapering region, and the ability to eliminate the support tether. However such an approach would be less robust to slight fiber misalignments arising from fabrication variability of the V-groove size on the order of 100 – 200 nm. These misalignments are small relative to the 10 μm mode diameter used in the reported device, but would cause substantial mode-mismatch in any scheme with a short waveguide taper. The optimal mode-matching of the junction would also likely be diminished, as increased mode confinement in the waveguide tip would render the profile less circularly symmetric.
  20. Q. Lin, J. Rosenberg, X. Jiang, K. Vahala, and O. Painter, “Mechanical Oscillation and cooling actuated by the optical gradient force,” Phys. Rev. Lett.103, 10360 (2009). [CrossRef]
  21. While in principle both intensity and phase noise of the laser can contribute to the heating of the mechanical mode, for an optically resonant measurement of position in the sideband unresolved regime the phase noise does not contribute to backaction and only intensity noise affects the mechanics. In this regime the phase noise adds a small component to the imprecision noise floor. Measurements of the phase and intensity noise of our laser reveal no excess intensity noise and a flat frequency NPSD of Sωω= 5 × 103rad2Hz in the frequency range of interest. Consequently, for the probe powers used in this work, the excess back-action due to technical laser noise is negligible, and the phase noise contribution to the noise floor lies roughly 60 dB below the shot noise.
  22. P. Rabl, C. Genes, K. Hammerer, and M. Aspelmeyer, “Phase-noise induced limitations on cooling and coherent evolution in optomechanical systems,” Phys. Rev. A80, 063819 (2009). [CrossRef]
  23. A. H. Safavi-Naeini, J. Chan, J. T. Hill, S. Gröblacher, H. Miao, Y. Chen, M. Aspelmeyer, and O. Painter, “Laser noise in cavity-optomechanical cooling and thermometry,” New J. Phys.15, 035007 (2013). [CrossRef]
  24. A. M. Jayich, J. C. Sankey, K. Bjorke, D. Lee, C. Yang, M. Underwood, L. Childress, A. Petrenko, S. M. Girvin, and J. G. E. Harris, “Cryogenic optomechanics with a Si3N4 membrane and classical laser noise,” New J. Phys.14, 115018 (2012). [CrossRef]
  25. T. P. Purdy, R. W. Peterson, and C. A. Regal, “Observation of radiation pressure shot noise on a macroscopic object,” Science339, 801–804 (2013). [CrossRef] [PubMed]
  26. C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, “Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes,” Phys. Rev. A77, 033804 (2008). [CrossRef]
  27. K. D. Bouwmeester and D. Bouwmeester, “Sub-kelvin optical cooling of a micromechanical resonator,” Nature444, 75–78 (2006). [CrossRef] [PubMed]

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