Storing optical information as a mechanical excitation in a silica optomechanical resonator.
ABSTRACT We report the experimental demonstration of storing optical information as a mechanical excitation in a silica optomechanical resonator. We use writing and readout laser pulses tuned to one mechanical frequency below an optical cavity resonance to control the coupling between the mechanical displacement and the optical field at the cavity resonance. The writing pulse maps a signal pulse at the cavity resonance to a mechanical excitation. The readout pulse later converts the mechanical excitation back to an optical pulse. The storage lifetime is determined by the relatively long damping time of the mechanical excitation.
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ABSTRACT: We present a nonrelativistic Hamiltonian of the interaction between a moving mirror and radiation pressure. This Hamiltonian is derived directly from the equation of motion of a moving mirror, and the wave equation with time-varying boundary conditions. We discuss the canonical quantization of both the field and the motion of the mirror.Physical Review A 04/1995; 51(3):2537-2541. · 3.04 Impact Factor
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ABSTRACT: We propose a scheme for transferring quantum states from the propagating light fields to macroscopic, collective vibrational degree of freedom of a massive mirror by exploiting radiation pressure effects. This scheme may prepare an Einstein-Podolsky-Rosen state in position and momentum of a pair of distantly separated movable mirrors by utilizing the entangled light fields produced from a nondegenerate optical parametric amplifier.Physical Review A - PHYS REV A. 01/2003; 68(1).
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ABSTRACT: We perform an analysis of the optomechanical entanglement between the experimentally detectable output field of an optical cavity and a vibrating cavity end-mirror. We show that by a proper choice of the readout (mainly by a proper choice of detection bandwidth) one can not only detect the already predicted intracavity entanglement but also optimize and increase it. This entanglement is explained as being generated by a scattering process owing to which strong quantum correlations between the mirror and the optical Stokes sideband are created. All-optical entanglement between scattered sidebands is also predicted and it is shown that the mechanical resonator and the two sideband modes form a fully tripartite-entangled system capable of providing practicable and robust solutions for continuous variable quantum communication protocols.Physical Review A 06/2008; · 3.04 Impact Factor
Storing light as a mechanical excitation in a silica optomechanical resonator
Victor Fiore1, Yong Yang1, Mark Kuzyk1, Russell Barbour1, Lin Tian2, and Hailin Wang1
1Department of Physics, University of Oregon, Eugene, Oregon 97403, USA
2Department of Physics, University of California, Merced, California 95343, USA
We report the experimental demonstration of optomechanical light storage in a silica
resonator. We use writing and readout laser pulses tuned to one mechanical frequency below
an optical cavity resonance to control the coupling between the mechanical displacement and the
optical field at the cavity resonance. The writing pulse maps a signal pulse at the cavity
resonance to a mechanical excitation. The readout pulse later converts the mechanical
excitation back to an optical pulse. The light storage lifetime is determined by the relatively
long damping time of the mechanical excitation.
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Light is a natural and ideal information carrier, but is difficult to store. Light storage is
important for all-optical information networks and is also an essential ingredient for long-
distance quantum communication1, 2. A variety of approaches for light storage have been
actively pursued. Storage of light as spin excitations in atomic media or as persistent atomic
excitations in inhomogeneously broadened solids has been realized in quantum as well as
classical regimes3-6. Optical pulses have also been stored in dynamically-tunable coupled-
resonator optical waveguides or as acoustic excitations in optical fibers7-10.
Optomechanical resonators, in which optical fields couple to mechanical oscillations via
radiation pressure (see Fig. 1a), provide another potential avenue for light storage.
Optomechanical interactions have been successfully explored for the control of mechanical as
well as optical processes in these resonators in the steady state11. Earlier experimental studies
have demonstrated optomechanical parametric amplification, laser cooling, and normal mode
splitting of a mechanical mode12-18. Optomechanical processes analogous to the well known
phenomenon of electromagnetically-induced transparency (EIT) have also been realized recently
in both optical and microwave regimes19-21.
Here, we report a proof-of-principle experimental demonstration of storing light as a
mechanical excitation in a silica resonator via transient optomechanical processes, with the
storage lifetime determined by the relatively long decay time of the mechanical excitation. In
comparison with atomic or spin systems, an optomechanical resonator features the remarkable
property that an optically-active mechanical mode can couple to any of the optical resonances
via radiation pressure. Optomechanical processes not only can store light at a given
wavelength as a mechanical excitation, but also can map the stored mechanical excitation back
to light at practically any desired wavelength22-25. This capability of wavelength conversion can
play a special role in both classical and quantum networks, for example, by converting optical
information from a given wavelength, including microwaves, to a wavelength that is suitable for
long distance communication, or by mapping photons emitted from one type of quantum system
to photons that can couple to another type of quantum system.
In addition, an optical pulse can also be localized and its spatial-temporal profile be stored
in an array of optomechanical resonators via processes analogous to those used in dynamically
tunable coupled-resonator optical waveguides7, as proposed recently26. In comparison with an
all-optical system, optical properties of an optomechanical system can be effectively controlled
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with optical pulses via radiation pressure. Mechanical oscillators with high quality factors can
also feature a storage lifetime much longer than that can be achieved with optical micro- or
For optomechanical light storage, we use “writing” and “readout” laser pulses tuned to one
mechanical frequency, ωm, below the optical cavity resonance to control the coupling between
the mechanical displacement and the optical field at the cavity resonance (see Fig. 1b). The
writing pulse maps a signal pulse at the cavity resonance to a mechanical excitation. The
readout pulse later converts the mechanical excitation back to an optical pulse at the cavity
resonance. As illustrated in Fig. 1a, in an optomechanical resonator, the displacement of a
mechanical oscillator modulates the frequency of an optical cavity mode, with
where x is the mechanical displacement and g is the optomechanical coupling coefficient. In
the limit that
κ ω >>
(the resolved sideband limit) and where κ is the cavity decay
rate and is the intracavity photon number for either the writing or the readout pulse, the
interaction between the mechanical displacement and the optical field at the cavity resonance
can be approximated as a coupled oscillator system, with an effective interaction Hamiltonian
given by , where and are the annihilation operators for the optical
field and the mechanical displacement, respectively, and
is the effective
optomechanical coupling rate with being the zero-point fluctuation for the mechanical
mode22. In this system, the writing and readout pulses can control or switch on/off the
effective optomechanical coupling between the optical field and the mechanical displacement.
As shown in Fig. 1c, for the storage process, a writing pulse couples a signal pulse to the
mechanical mode, generating a mechanical excitation. For the retrieval process, a readout
pulse couples the stored mechanical excitation to the cavity mode, mapping the mechanical
excitation back to an optical pulse.
We used silica microspheres as a model system for an optomechanical resonator18.
Deformed silica microspheres with a deformation near 2% and a diameter near 30 μm were
fabricated by fusing together two non-deformed microspheres of similar sizes with a CO2 laser.
The small deformation enables free-space evanescent excitation of whispering gallery modes
(WGMs) near the sphere equator, with a coupling efficiency of 9% for resonant excitation. A
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breathing mode of the sphere with (n, l) = (1, 2), where n and l are the radial and angular mode
numbers, respectively, was used as the mechanical oscillator. For the experiments presented in
ω /2π = 108.4 MHz,
γ /2π = 38 kHz, and κ/2π = 40 MHz, as determined from
displacement power spectra and optical transmission spectra.
The writing, readout, and signal pulses with a wavelength near 800 nm were all derived
from the same laser beam generated from a tunable Ti:Sapphire ring laser. The writing and
readout pulses, with the same frequency, ωl, were obtained by gating the laser beam with an
acousto-optic modulator (AOM). The laser pulses propagated through an electro-optic
modulator (EOM), with the electro-optic phase modulation synchronized with the writing pulse
(there is no phase modulation for the readout pulse). The higher frequency sideband generated
by the phase modulation served as the signal pulse. The frequency of the signal pulse, ωs, is
locked to a given WGM resonance with a Pound-Drever-Hall technique. The timing and
temporal profile of the signal pulse is the same as those of the writing pulse. The intracavity
peak power of the signal pulse is kept below 1% of that of the writing and readout pulses.
Unless otherwise specified, we set the EOM modulation frequency to
and have used the pulse sequence shown in the inset of Fig. 2a. All experiments
were carried out at room temperature.
Incident writing and readout pulses were also used as the local oscillator for the heterodyne
detection of signal and retrieved pulses emitted from the optical resonator, respectively. Since
the signal pulse is generated directly from the writing pulse with an electro-optic phase
modulation, the heterodyne detection is not sensitive to the part of the signal pulse that is not
emitted from the optical resonator. A spectrum analyzer in a time-gated detection mode was
used for time-resolved heterodyne detection, with the time resolution limited by the resolution
bandwidth (1 MHz) as well as the gate length (3 μs). More experimental details along with a
diagram for the experimental setup are described in the supplementary materials.
Figure 2 presents a proof-of-principle experimental demonstration of optomechanical light
storage. Figure 2a shows the heterodyne-detected signal and retrieved pulses emitted from the
silica resonator. In this experiment, the readout pulse, which arrives 6.5 μs after the center of
the signal pulse, interacts with the mechanical excitation induced by the signal and the writing
pulse, generating the retrieved pulse. The incident writing and readout pulses produce an
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estimated intracavity photon number of nc = 1.5x106, corresponding to a peak optomechanical
coupling rate of G0/2π = 2 MHz. To determine the light storage lifetime, we plot in Fig. 2b the
energy of the retrieved pulse, obtained from measurements similar to those shown in Fig. 2a, as
a function of the delay between the writing and the readout pulse. The pulse energy decays
exponentially as a function of the delay, yielding a storage lifetime of 3.5 μs, which is in good
agreement with the mechanical linewidth,
γ /2π = 38 kHz, obtained from the displacement
The temporal profiles of the signal and retrieved pulses shown in Fig. 2a are significantly
modified by the time resolution of the heterodyne detection measurement and by the temporal
profile of the local oscillators (i.e., the writing and readout pulses). Figure 2c shows the
heterodyne-detected retrieved pulse with the durations of the readout pulse increasing
incrementally from 0.3 μs to 1.4 μs, indicating that the time-resolution of the heterodyne
measurement is approximately 3 μs. The powers obtained in these transient measurements are
effectively the average power over a given detection period.
Optomechanical storage and retrieval processes are characterized by their distinct
dependence on the intensity of the writing and readout pulses and on the detuning between the
signal and writing/readout pulses. Figure 3a shows the dependence of the retrieved pulse
energy on the relative readout intensity, I/I0, with I0 corresponding to G0/2π=0.7 MHz. Similar
highly nonlinear dependence was also observed when the writing intensity was varied.
Figure 3b shows the retrieved pulse energy as a function of the detuning between the signal and
the writing/readout pulses at two different readout intensities, with ωs fixed at the cavity
resonance. For Figs. 3a and 3b, the writing intensity is fixed at I0 and the duration of the
readout pulse is 3 μs. The observed resonance in Fig. 3b centered at
the optomechanical origin of the light storage and retrieval processes. As shown in Fig. 3b, the
spectral lineshape observed is independent of the intensity of the readout pulse. The same
spectral lineshape was also observed at higher readout intensities.
The experimental results in Figs. 2 and 3 are in good agreement with the theoretical
calculation, for which we used the coupled oscillator equations to describe the optomechanical
coupling between the mechanical displacement and the optical field at the cavity resonance (see
the supplementary material), with all parameters determined by the experiments. Figure 3c
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