Microcavity phonoritons a coherent optical-to-microwave interface A. S. Kuznetsov1K. Biermann1A. Reynoso2 3 4A. Fainstein2 3and P. V. Santos1 1Paul-Drude-Institut f ur Festk orperelektronik

2025-05-02 0 0 5.06MB 40 页 10玖币
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Microcavity phonoritons – a coherent optical-to-microwave interface
A. S. Kuznetsov*,1K. Biermann,1A. Reynoso,2, 3, 4 A. Fainstein,2, 3 and P. V. Santos1
1Paul-Drude-Institut f¨ur Festk¨orperelektronik,
Leibniz-Institut im Forschungsverbund Berlin e. V.,
Hausvogteiplatz 5-7, 10117 Berlin, Germany ∗
2Centro At´omico Bariloche & Instituto Balseiro (C.N.E.A.)
and CONICET, 8400 S.C. de Bariloche, R.N., Argentina
3Instituto de Nanociencia y Nanotecnolog´ıa (INN-Bariloche),
Consejo Nacional de Investigaciones Cient´ıficas y T´ecnicas (CONICET)-CNEA,8400 Bariloche, Argentina
4Departamento de F´ısica Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
(Dated: October 27, 2022)
Optomechanical systems provide a pathway for the bidirectional optical-to-microwave intercon-
version in (quantum) networks. We demonstrate the implementation of this functionality and non-
adiabatic optomechanical control in a single, µm-sized potential trap for phonons and exciton-
polariton condensates in a structured semiconductor microcavity. The exciton-enhanced optome-
chanical coupling leads to self-oscillations (phonon lasing) – thus proving reversible photon-to-
phonon conversion. We show that these oscillations are a signature of the optomechanical strong
coupling signalizing the emergence of elusive phonon-exciton-photon quasiparticles – the phonori-
tons. We then demonstrate full control of the phonoriton spectrum as well as coherent microwave-
to-photon interconversion using electrically generated GHz-vibrations and a resonant optical laser
beam. These findings establish the zero-dimensional polariton condensates as a scalable coher-
ent interface between microwave and optical domains with enhanced microwave-to-mechanical and
mechanical-to-optical coupling rates.
Introduction
Coherent interactions between microwave (GHz) phonons and optical (hundreds of THz) photons enable
the control of opto-electronic phenomena at the nano- and ps-scale, interconversion of optical and mi-
crowave photons for communication between distant qubits [1–3] as well as optical information transfer in
on-chip computational devices [4,5]. One strategy towards efficient interconversion uses optomechanical
interactions [6], i.e., correlations between optical and mechanical degrees of freedom. In this setting,
optomechanical systems relying on the coupling between high-frequency vibrations (phonons) and solid-
state excitations have become relevant for advanced photonic applications, including the emerging fields
of quantum communication [7] and control of various quantum states [8–14], e.g., qubits [15].
In general, coherent interactions between photons and phonons require a large coupling energy as well
as low phonon (ΓM) and photon (γphot) decoherence rates. High-efficiency coherent transduction between
the particles presupposes a single-photon cooperativity
C0=4×g2
0
γphot ×ΓM
(1)
exceeding unity, where g0is the single-photon optomechanical coupling rate. If, in addition, g0>
{γphot,ΓM}, the phonon-photon interaction enters the optomechanical strong-coupling (OSC) regime [6],
where a novel optomechanical quasiparticle emerges – the phonoriton [16]. The above requirements
become relaxed for photon populations Nphot >1, for which C0is enhanced by a factor Nphot.
∗Corresponding author, e-mail: kuznetsov@pdi-berlin.de
arXiv:2210.14331v1 [physics.optics] 25 Oct 2022
2
Reaching the OSC regime in the solid-state faces several challenges imposed by the huge mismatch
between the phonon (fM) and the photon (fphot) frequencies fM<< fphot, typically large values of ΓMand
γphot, dissimilar spatial dimensions (wavelengths) of the optical and phonon modes, and low magnitudes of
g0. In this context, polaromechanical systems – optomechanical setups utilizing strongly coupled excitons
and photons (simply, polaritons [17] or MPs) in monolitic microcavities (MCs) – become an attractive
option [18]. These systems benefit from the large deformation potential exciton-phonon coupling and the
simultaneous confinement of photons and phonons [19,20], enabling coherent polaromechanics [21,22]
with near-unity single-polariton cooperativity [23].
In this work, we first demonstrate the OSC between Bose-Einstein condensates (BECs) of polaritons
and GHz phonons confined in µm-sized potential traps within a semiconductor MC. This OSC results
in phonoritons, which are evidenced by optomechanical self-oscillations (SOs) or phonon lasing. The
SOs can be accounted for by the deformation potential coupling between the BEC pseudo-spin states
mediated by the phonons. We then show that phonoritons can also be stimulated and controlled by
piezoelectrically generated GHz phonons as well as optically. Thus, we establish these traps as a scalable
and bidirectional optical-to-microwave interface. The implications of these milestones for the coherent
control down to the quantum regime are discussed.
Results
The studies were carried out using an (Al,Ga)As MC with intracavity traps [24] for phonons and polaritons
(cf. Fig. 1a, further details in Methods). These traps confine λC=λ∗nc= 810 nm photons (ncis the
average refractive index of the MC spacer) as well acoustic phonons with wavelenghts of 3λand λ. The
relevant confined phonons have either longitudinal (LA) or transverse (TA) preferential polarizations
with frequencies f(3λ)
LA = 7 GHz and f(λ)
LA = 20 GHz for the LA modes and f(iλ)
TA ≈0.7×f(ηλ)
LA (η= 1,3)
for the TA ones (see SM-V-B). Here, 0.7 is the ratio between the TA and LA sound velocities along
the MC z[001]-direction. The above implies that f(λ)
TA ≈2×f(3λ)
LA . Finally, a ring-shaped piezoelectric
bulk acoustic wave resonator fabricated on the top surface electrically injects long-lived (1/ΓM≈300 ns)
monochromatic LA phonons with frequency tunable around f(3λ)
LA = 7 GHz [25]. Figure 1(c) displays
a spatial photoluminescence (PL) map of the sample. The bright PL spot close to the center of the
resonator ring-shaped aperture corresponds to the emission of the trap. Its PL at low optical excitation
power (PExc) displays discrete energy spectrum typical of a particle in a box. The transition to the
BEC at high PExc is accompanied by an energy blueshift and a nonlinear increase of the PL intensity, as
detailed in SM-II-B. Simultaneously, the linewidth reduces to a record-low value γMP ≈0.5 GHz f(3λ)
LA ,
cf. Fig.1(c), which enables the non-adiabatic interaction regime. Dependence of γMP on PExc is detailed
in SM-III-B. In the following we consider two 4 ×4µm2traps with different polariton excitonic content
of 0.05 (labelled T1) and 0.2 (labelled T2).
Optomechanical self-oscillations in single traps. Signatures of the polariton-phonon interaction
can be readily identified in spectral PL maps of the trap T2ground state (GS) recorded in the BEC regime
for increasing PExc (cf. Fig. 1f). The energy axis is referenced to the main emission line (the zero-phonon
line, ZPL). For PExc <200 mW, the map shows, in addition to the ZPL, a second line displaced by
∼2.3×f(3λ)
LA , which evidences the splitting of the trap GS into two components. The GS degeneracy
3
can be lifted in an asymmetric trap (i.e., non-square) by the non-vanishing effective in-plane momentum
induced by the confinement via the so-called longitudinal-transverse pseudo-spin splitting [26], described
in SM-V-A. In the BEC state, the splitting can be amplified by polariton-polariton interactions between
unequally populated pseudo-spin states.
Figure 1f reveals two remarkable optomechanical features for PExc >200 mW: the locking of the
pseudo-spin state at f(λ)
TA and the emergence of sidebands separated by multiples of f(3λ)
LA . The latter are
indicated by the blue arrows in an exemplary profile for PExc = 320 mW in Fig. 1d. These sidebands are
attributed to phonon self-oscillations (SOs) – the excitation of a coherent mechanical motion by a time-
independent polariton drive. The stimulated phonons backact on polaritons by locking their pseudo-spin
splitting to f(λ)
TA . We can estimate the optomechanical coupling rate (g) leading to the sideband formation
by taking into account the fact that the amplitude of the nth sideband is proportional to J2
n(g/f(3λ)
LA ),
where Jnis the Bessel function of the nth order [22]. We point out that the ratio of the peak intensities
of the sideband at E/hf (3λ)
LA = 1 and the ZPL is J2
1/J2
0≈0.3. This ratio implies that g∼f(3λ)
LA . Thus,
g > {ΓM, γMP}, which confirms the OSC character of the coupling and gives a lower estimate of C≈104
according to Eq. 1. Therefore, the OSC evidences the formation of a phonon-exciton-photon quasiparticle
– the phonoriton [16]. Interestingly, phonoritons involving λand 3λphonons can appear simultaneously,
indicating that more than one phonon mode can enter the OSC regime.
The pseudo-spin locking at f(λ)
TA (rather than at 2 ×f(3λ)
LA ) is further corroborated by the GS PL from
polaritons with a reduced exciton content, as illustrated for the trap T1in Fig. 1c. The PL from the
pseudo-spin state is weaker and sidebands are not observed. The GS splitting remains, nevertheless, locked
at f(λ)
TA over a wide range of excitation powers (cf. additional data in Fig. SM-6). SOs are ubiquitous in
optomechanics [27,28]. In polariton systems, they have been reported for processes of optoelectronic [29]
and optomechanical [30] nature. In contrast to the former, the SOs demonstrated here involve transitions
between the GS pseudo-spin states rather than between confined levels with different orbitals and larger
energy separation. Unlike the report [22] – in the present case, SOs are of the first-order nature and,
more importantly, emerge in a single trap rather than in an array.
The optomechanical couping between the GS pseudo-spin states leading to SOs requires confined
phonons with shear strain components, which are intrinsic for TA modes but absent in bulk LA ones
propagating along [001] GaAs. However, if the traps are not perfectly square, the lateral confinement
imparts a small shear component to the confined LA modes, which is proportional to the trap asymmetry
as shown in SM-V-C. Furthermore, a first-order deformation potential interaction between phonons and
polaritons of the split GS can provide both the interlevel coupling (g0,↑↓), corresponding to the coupling
between the pseudo-spins, which is required to trigger SOs, as well as the intralevel one (g0,↑↑) leading
to energy modulation and sideband formation. These coupling rates for the TA and LA confined modes
are summarized in Table SM-V for a trap with a= 4 µm and asymmetry ∆a/a = 0.1. In essence, for
the GS, the interlevel coupling is considerably higher for TA modes g0,↑↓,TA ≈1 MHz ≈35 ×g0,↑↓,LA.
Hence, TA-like f(λ)
TA -phonoritons can form for polariton populations NMP ≤1000, significantly lower
than the BEC threshold of ∼105−106, as estimated in SM-II-C. Since g0,↑↑,TA is negligible for the TA
modes, TA-related SOs are normally not accompanied by sidebands. In contrast, LA-like SOs are usually
4
accompanied by sidebands due to the large on-site coupling energy g0,↑↑,LA ≈7 MHz, but require a large
BEC population. These predictions are in qualitative agreement with the results in Figs. 1c and 1d.
Phonoriton formation also requires a pseudo-spin energy splitting ∆Ematching the phonon energy.
The following picture emerges for the onset of the phonoriton-related SOs: ∆Edepends on the trap
geometry and can change with polariton density to match the phonon energy and trigger a particular
phonoriton mode. The matched phonon mode may vary with PExc leading to the behaviour illustrated
in Fig. 1f. The energy locking between the pseudo-spin states is attributed to the phonon-mediated
transfer of particles between them. The strong dependence of the transfer on ∆Etends to equilibrate
the difference in populations leading to the locking [31,32].
Lastly, SOs can also be induced by interactions between higher-energy (excited) BEC and phonon
modes. Some of these phonons can trigger oscillations with just a few polaritons (cf. Table SM-V and
the discussion in SM-V-D), thus opening the way to SO in the single-particle regime. Furthermore,
phonons also affect non-linear polariton interactions [33,34], including those involving the excitonic
reservoir [29,35]. Combined with the optomechanical coupling proposed here, these mechanisms may
additionally enhance the polaromechanical coupling.
Electrically stimulated sidebands. A unique feature of our platform is the ability to electrically
inject GHz LA bulk acosutic waves (BAWs) into traps using bulk acoustic wave resonators (BAWRs).
Figure 1e shows a spectrum of the trap T2under the modulation by f(3λ)
LA = 7 GHz phonons generated
by the BAWR driven with radio frequency (RF) voltage. One now observes well-defined and symmetric
sidebands separated by f(3λ)
LA . This demonstrates the non-adiabatic control of the polariton BEC by the
tunable phonon amplitude.
The evolution of the PL spectrum of the trap T1for increasing acoustic amplitudes ABAW is illustrated
by the color map of Fig. 2a and cross-sections in Fig. 2b-e. ABAW is expressed in terms of the square-
root of the nominal RF power (P0.5
RF ) applied to the BAWR. Spectra at low acoustic amplitudes P0.5
RF <
0.01 W0.5are dominated by the strong ZPL with a weaker pseudo-spin state locked at f(λ)
TA ≈2×f(3λ)
LA
indicated by the red arrow in Fig. 2b. At P0.5
RF ≈0.01 W0.5, the first two symmetric sidebands appear on
either side of the ZPL. At higher acoustic amplitudes, additional symmetric sidebands emerge, reaching
up to ±5×f(3λ)
LA -sidebands. For the intermediate P0.5
RF values, such as in Fig. 2d, the intensity of the ZPL
line becomes strongly suppressed. This suppression is a form of optomechanically induced transparency.
The solid blue lines in Figs. 2b-e are fits given by a sum of Lorentzians with linewidths (δE) weighted
by squared Bessel functions J2
n(χ), where χ– is the modulation amplitude (see SM-IV-B). The fits
show that the acoustic modulation redistributes the oscillator strength (initially at the ZPL) among
the sidebands while conserving the overall PL intensity. Figure 2g shows the dependence of the fitted
sideband linewidths δE on the normalized ABAW. Remarkably, δE(ABAW) sharply decreases by a factor
of two from δE(0.1) = 0.2×f(3λ)
LA to δE(0.2) = 0.1×f(3λ)
LA and then remains constant. The reduction
coincides with the appearance of the first sidebands, i.e., when χ≈f(3λ)
LA , cf. Fig. 2f. A similar linewidth
reduction is also observed for the first excited state of the trap (SM-IV-C ).
The OSC between particles with largely dissimilar lifetimes leads to quasiparticles with lifetimes ap-
proximately twice the one of the shorter-lived component. Such a behavior has been previously reported
5
for quasiparticles resulting from the strong-coupling of excitons and photons [36], photons and phonons [6],
as well as phonons and superconducting qubits [37], but not between polaritons and phonons. Stimulated
multimode OSC has been recently demonstrated for a system of two optical modes coupled to multiple
mechanical modes and driven using an external laser [38]. In contrast, in this work, polariton BEC states
are intrinsic to the MC. Conceptually, the RF-generated phonon field drives coherent oscillations between
the polariton states. In the weak-coupling limit, the states do not swap before decaying with the rate
γMP = 1.4 GHz. In the OSC limit, one enters the stimulated phonoriton regime, where the condensate
swaps between the pseudo-spin states at a rate γMP. In effect, phonoritons spend half of the time as
phonons with ΓMγMP, thus leading to a decay rate γMP/2. The linewidth narrowing thus directly
proves phonoriton stimulation.
The above picture can be described using the Hamiltonian (derived in SM-V-E ) for a phonon mode
ΩM= 2πf(3λ)
LA and two BEC modes ωiwith i = {l,u}for the lower energy and the upper energy mode of
the spin-split GS, respectively:
ˆ
H=~ΩMˆ
b†ˆ
b+X
i=l,u
~ωiˆa†
iˆai+ˆ
Hint.
The interaction term ˆ
Hint =~G2ˆa†
uˆal+ ˆa†
lˆauˆ
b†+ˆ
b2couples two BEC states separated by 2 ×
~ΩM. The ˆ
Hint is quadratic in phonon amplitude ˆ
b†+ˆ
b2, since the pseudo-spin splitting matches twice
the energy of the injected phonons, and the coupling strength is tuned by the amplitude of the injected
BAW. A detailed analysis of the interaction (cf. SM-V-E ) yields a coupling strength g2= 2√NMPnbG2,
where NMP and nbare the polariton and RF-generated phonon populations, respectively, and G2=g∆×
g0,↑↓/f(3λ)
LA , where we assumed g∆≈g0,↑↑, see SM-V-E. Now, the OSC condition becomes g2> γMP/4.
This model predicts a linewidth δE = 2 ×Im[j×γMP/4 + pg2
2−γ2
MP]/γMP with j=√−1, which is
displayed by the solid line in Figure 2g. In the calculations, we used the experimentally determined
polariton and phonon decay rates γMP = 1.4 GHz, ΓM= 3 MHz, respectively, and an estimated BEC
population NMP = 5 ×106. The phonon population nbwas determined for each ABAW as described in
SM-II-E. The calculations reproduce well the linewidth narrowing. However, the fitted G2value is ∼30
times larger than the one deduced for the pure optomechanical rates in the Table SM-V. The required
coupling enhancement can be provided by some of the mechanisms listed at the end of the previous
section.
Coherent optical control of phonoritons. Finally, we demonstrate optical control of phonoritons
in a trap using the setup depicted in Fig. 3a, which is complementary to the mechanical control addressed
in the previous section. For that purpose, a weak single-mode control laser with tunable energy ∆Lwas
scanned with energy steps of 2.3 GHz across the GS of the trap T1. PL spectra were then recorded for
each ∆Las displayed in Fig. 3b. The weak curved stripes separated by f(3λ)
LA (indicated by the small
yellow arrows) are the phonon sidebands due to the modulation by RF-generated phonons. The weak
diagonal feature indicated by the blue dashed arrow is the Rayleigh scattering of the control laser as it
was scanned from positive to negative values of ∆L. Interestingly, the sidebands redshift by as much as
0.2×f(3λ)
LA when the control laser is within their spectral range, i.e., for |∆L| ≤ 5×f(3λ)
LA . This relatively
large red-shift is attributed to a renormalization of the phonoriton GS energy under the increased phonon
摘要：

Microcavityphonoritons{acoherentoptical-to-microwaveinterfaceA.S.Kuznetsov*,1K.Biermann,1A.Reynoso,2,3,4A.Fainstein,2,3andP.V.Santos11Paul-Drude-InstitutfurFestkorperelektronik,Leibniz-InstitutimForschungsverbundBerline.V.,Hausvogteiplatz5-7,10117Berlin,Germany2CentroAtomicoBariloche&InstitutoBa...

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Microcavity phonoritons a coherent optical-to-microwave interface A. S. Kuznetsov1K. Biermann1A. Reynoso2 3 4A. Fainstein2 3and P. V. Santos1 1Paul-Drude-Institut f ur Festk orperelektronik.pdf

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