Cavity optomechanics reached remarkable success in coupling optical and mechanical degrees of freedom. The standard mechanism relies on dispersive interaction wherein a cavity mode acquires a frequency shift proportional to the mechanical displacement. Efficient coupling is, however, often impeded by large cavity decay rates or strong heating of the mechanical element by optical absorption. In this talk, I will present two strategies to circumvent this problem. In the first one, a membrane doped with an ensemble of two-level emitters or patterned with a photonic-crystal structure is used as a mechanical element. The hybridization of the cavity mode with the membrane’s internal resonance leads to a modified response, resulting in an effective narrow cavity linewidth. I will show how such systems can be described quantum mechanically and discuss how optomechanical sideband cooling can be improved by the presence of the internal resonance. Second, I will discuss optomechanics with levitated particles and show how coherent scattering can be used to generate strong mechanical squeezing. In this system, the standard dispersive interaction is replaced by scattering of the trapping beam into an empty cavity mode. This process can result in strong, controllable coupling between the cavity mode and the motion of the particle with minimal absorption heating. I will also briefly outline how this type of interaction can be used to engineer coupling between different center-of-mass modes of the particle allowing, in principle, full optomechanical control of the particle motion.

1. Improved optomechanical interactions for quantum
technologies
Ondřej Černotík
Department of Optics, Palacký University Olomouc, Czechia
Joint Quantum Institute, 8 October 2019
From hybrid membranes to optical levitation
@cernotik

2. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Nonreciprocal devices
Z. Shen et al., Nat. Commun. 9, 1797 (2018)
Cavity optomechanics represents a mature platform for
quantum technologies.
2
R. Andrews et al., Nature Phys. 10, 321 (2014)
Transduction Sensing
LIGO, PRL 116, 061102 (2016)

3. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Optomechanical interaction is due to radiation pressure.
3
M. Aspelmeyer, T. Kippenberg, and F.
Marquardt, RMP 86, 1391 (2014)
Hamiltonian: H = !c(x)a†
a + !mb†
b<latexit sha1_base64="dd7FVu9ATyMApBK+CeQbs1kg5/k=">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</latexit>
H = !ca†
a + !mb†
b + g0a†
a(b + b†
)<latexit sha1_base64="S225tzZzq47yt0PZPvTCBbgcKco=">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</latexit>
Cavity frequency: !c(x) ⇡ !c +
d!c
dx
x
<latexit sha1_base64="IXdhICO91MyTEVWvEyXgkSOPxXM=">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</latexit>
Coupling strength: g0 =
d!c
dx
xzpf =
!c
L
xzpf
<latexit sha1_base64="HYo3whsPlsqloPSF3r7qSOkK8vI=">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</latexit>
x = xzpf (b + b†
)<latexit sha1_base64="iYClzAi4BkNGQGGXHPfO5TBUhAM=">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</latexit>
ˆa
ˆx
!m
!c

4. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Strong coupling can be achieved by suitable driving.
4
M. Aspelmeyer, T. Kippenberg, and F.
Marquardt, RMP 86, 1391 (2014)
Optomechanical coupling is weak g0 ⌧ <latexit sha1_base64="T65oHrLye7ZYDdmoSxGl1ko4Yn4=">AAACFXicbVDLSsNAFJ3UV42vqks3wSK4KCWJBV2WutBlFfuAJoTJdNoOnTyYuRFLyE+48VfcuFDEreDOv3GadqGtBy4czrn3zp3jx5xJMM1vrbCyura+UdzUt7Z3dvdK+wdtGSWC0BaJeCS6PpaUs5C2gAGn3VhQHPicdvzx5dTv3FMhWRTewSSmboCHIRswgkFJXqniAH2AfE/v9qrhprZtVmzbVlXLUn3omQ7nzhjHMdYzr1Q2q2YOY5lYc1JGczS90pfTj0gS0BAIx1L2LDMGN8UCGOE0051E0hiTMR7SnqIhDqh00/yazDhRSt8YREJVCEau/p5IcSDlJPBVZ4BhJBe9qfif10tgcOGmLIwToCGZPTRIuAGRMY3I6DNBCfCJIpgIpm41yAgLTEAFqasQrMUvL5O2XbXOqvZNrVxvzOMooiN0jE6Rhc5RHV2jJmohgh7RM3pFb9qT9qK9ax+z1oI2nzlEf6B9/gAospzr</latexit>
Solution: strong optical drive a ! ↵ + a, g0 ! g = g0↵<latexit sha1_base64="Uv5av/BauRr+6HaUJ3i2Un4px08=">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</latexit>
Interaction Hamiltonian Hint = g0a†
a(b + b†
) ! g(a + a†
)(b + b†
)<latexit sha1_base64="0MfHSOQNZXhzBE8bw9IHcH2lZU8=">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</latexit>

5. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Driving frequency is an important control parameter.
5
Resonant drive:
Position readoutHint = g(a + a†
)(b + b†
)<latexit sha1_base64="56sSN8EesOA3qfjnR4QDA88tXP8=">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</latexit>
!L = !c<latexit sha1_base64="FJUPRTyPlOiLi8BRgnLyu6T+khs=">AAACHHicbVC7SgNBFJ2Nr7i+opY2g0GwkLC7CWgjiBZaWEQxGkiWMDu5iUNmH8zcFcOSD7HxV2wsFLGxEPwbJ3ELXwcuHM65986dEyRSaHScD6swNT0zO1ectxcWl5ZXSqtrlzpOFYcGj2WsmgHTIEUEDRQooZkoYGEg4SoYHI39qxtQWsTRBQ4T8EPWj0RPcIZG6pSqbYRbnOxpnR8f+pnnOTue55mqjTK7HYfQZ51Tuk9zyu1Rp1R2Ks4E9C9xc1ImOeqd0lu7G/M0hAi5ZFq3XCdBP2MKBZcwstuphoTxAetDy9CIhaD9bHLUiG4ZpUt7sTIVIZ2o3ycyFmo9DAPTGTK81r+9sfif10qxt+dnIkpShIh/PdRLJcWYjpOiXaGAoxwawrgS5lbKr5liHE2etgnB/f3lv+TSq7jVindWKx8c5nEUyQbZJNvEJbvkgJyQOmkQTu7IA3kiz9a99Wi9WK9frQUrn1knP2C9fwLTAJ9S</latexit>
!
!c = !L

Blue-detuned drive:
SqueezingHint ⇡ g(ab + a†
b†
)<latexit sha1_base64="5a9KoSOd819KJZzLEQ30Gkh5QgI=">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</latexit>
!L = !c + !m<latexit sha1_base64="I1Hkj2aAQs5txEO5LbX1CIkZBSw=">AAACJXicbZDLSsNAFIYn3o23qks3g0UQlJJEQRcKogtduKhiVWhDmUxP6+BMEmZOxBL6Mm58FTcuLCK48lWc1iy8HTjw8Z/LnPmjVAqDnvfujIyOjU9MTk27M7Nz8wulxaVLk2SaQ40nMtHXETMgRQw1FCjhOtXAVCThKro9GtSv7kAbkcQX2E0hVKwTi7bgDK3ULO01EO5xuKd+fnwY5kHgbQZBYHO7l7uNREGHNU/pPi2QbxSg3F6zVPYq3jDoX/ALKJMiqs1Sv9FKeKYgRi6ZMXXfSzHMmUbBJfTcRmYgZfyWdaBuMWYKTJgPr+vRNau0aDvRNmOkQ/X7RM6UMV0V2U7F8Mb8rg3E/2r1DNu7YS7iNEOI+ddD7UxSTOjAMtoSGjjKrgXGtbC3Un7DNONojXWtCf7vL/+Fy6Dib1WCs+3ywWFhxxRZIatknfhkhxyQE1IlNcLJA3kiL6TvPDrPzqvz9tU64hQzy+RHOB+f4AejCA==</latexit>
!m
!!c !L
 < !m
Red-detuned drive:
State swapHint ⇡ g(a†
b + b†
a)<latexit sha1_base64="C2cL4zLTxQ0Tc/A5a3Ydvv5J6ak=">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</latexit>
!L = !c !m<latexit sha1_base64="xGnx2CRz/5wZq96nyOinQrriuyY=">AAACJXicbZDLSsNAFIYn3o23qks3g0VwoSWJgi4URBe6cFHFqtCGMpme1sGZJMyciCX0Zdz4Km5cWERw5as4rVl4O3Dg4z+XOfNHqRQGPe/dGRkdG5+YnJp2Z2bn5hdKi0uXJsk0hxpPZKKvI2ZAihhqKFDCdaqBqUjCVXR7NKhf3YE2IokvsJtCqFgnFm3BGVqpWdprINzjcE/9/PgwzIPA2wiCwOZ2L3cbiYIOa57SfVog3yxAub1mqexVvGHQv+AXUCZFVJulfqOV8ExBjFwyY+q+l2KYM42CS+i5jcxAyvgt60DdYswUmDAfXteja1Zp0XaibcZIh+r3iZwpY7oqsp2K4Y35XRuI/9XqGbZ3w1zEaYYQ86+H2pmkmNCBZbQlNHCUXQuMa2FvpfyGacbRGutaE/zfX/4Ll0HF36oEZ9vlg8PCjimyQlbJOvHJDjkgJ6RKaoSTB/JEXkjfeXSenVfn7at1xClmlsmPcD4+AeMjowo=</latexit>
!m
!
!c!L
 < !m

6. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Optomechanical interaction can be observed in various
systems.
6
Membrane in the middle
J. Sankey et al., Nat. Phys. 6, 707 (2010)
Optomechanical crystals
M. Eichenfield et al., Nature 462, 78 (2009)
Levitation
T. Li et al., Nat. Phys. 7, 527 (2011)
Suspended mirrors
S. Gröblacher et al., Nat. Comm. 6, 7606 (2015)
Electromechanics
J.D. Teufel et al., Nature
475, 359 (2011)

7. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Functionality of optomechanics can be enhanced by
coupling to other systems.
7
Atoms
A. Jöckel et al., Nature Nano 10, 55 (2015)
Bose–Einstein condensates
P. Treutlein et al., PRL 99, 140403 (2007)
Color centers
O. Arcizet et al., Nature Physics 7, 879 (2011)
Superconducting systems
Y. Chu et al., Science 358, 199 (2017)

8. Improved optomechanical interactions
Optical levitation with coherent scattering
Cavity optomechanics with hybrid membranes

9. Cavity optomechanics with hybrid membranes
Aurélien Dantan
University of Aarhus
Claudiu Genes
MPI Erlangen
OC, A. Dantan, C. Genes, PRL 122, 243601 (2019)ˇ
OC, C. Genes, A. Dantan, QST 4, 024002 (2019)ˇ

10. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Optomechanical interaction can cool mechanical motion
to its ground state.
10
H = c†
c + !mb†
b + g(b + b†
)(c + c†
)<latexit sha1_base64="QJ1dF9yNCo74QnY9XtuUmhQF8T8=">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</latexit>
˙x = !mp, ˙p = !mx p + ⇠ + F<latexit sha1_base64="IPY+ABxs2KRbLm0PKBFgR9kNGCY=">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</latexit>
F = g(c + c†
)<latexit sha1_base64="vKGcHJXkh4XwQnfwqI9XrK/p/GM=">AAACG3icbVDLSgNBEJz17fqKevQyGISIEnZXQS+CKKjHKEaFZA2zk846OPtgplcMS/7Di7/ixYMingQP/o2Tx0GjBQ1FVXdPTwWpFBod58saGR0bn5icmrZnZufmFwqLSxc6yRSHKk9koq4CpkGKGKooUMJVqoBFgYTL4Paw61/egdIiic+xnYIfsTAWLcEZGqlR8OoI99jbUzs7PvBzz3M2Pc8ztd3J7SO6R8MS3+DX9SYLQ1DrdqdRKDplpwf6l7gDUiQDVBqFj3oz4VkEMXLJtK65Top+zhQKLqFj1zMNKeO3LISaoTGLQPt576YOXTNKk7YSZSpG2lN/TuQs0rodBaYzYnijh72u+J9Xy7C16+ciTjOEmPcfamWSYkK7QdGmUMBRtg1hXAlzK+U3TDGOJk7bhOAOf/kvufDK7lbZO90u7h8M4pgiK2SVlIhLdsg+OSEVUiWcPJAn8kJerUfr2Xqz3vutI9ZgZpn8gvX5DdUQniQ=</latexit>
cool =
1
2
[SF (!m) SF ( !m)]
<latexit sha1_base64="S1ncTwH7x75Mn/2jUzYUkXk5W6s=">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</latexit>
F. Marquardt et al., PRL 99, 093902 (2009)
SF (!) =
g2

2 + (! )2
<latexit sha1_base64="TppRzcFD7hwJoHfC84sIgyGSBDw=">AAACQ3icbVDLbhMxFPWUVxkeDbBkYxEhtQKiGVMJNkhVQS3L8khbkZlEd5w7qRXPQ/YdRDSaf2PDD7DrD7BhUVR1W6lOMgtoOdKVj865174+SamVpSA49lauXb9x89bqbf/O3Xv31zoPHu7bojIS+7LQhTlMwKJWOfZJkcbD0iBkicaDZPp27h98RWNVkX+mWYlxBpNcpUoCOWnU+RIRfqPFPYOPu9txLUTwXAjharOp/U+jnfWoyHACG/wNj1IDsp4MRTSFsoSmXp5D8axtehG9Q02wMRSN34w63aAXLMCvkrAlXdZib9T5GY0LWWWYk9Rg7SAMSoprMKSkxsaPKoslyClMcOBoDhnauF7s3vCnThnztDCucuIL9e+JGjJrZ1niOjOgI3vZm4v/8wYVpa/jWuVlRZjL5UNppTkVfB4oHyuDkvTMEZBGuV25PAIXFLnYfRdCePnLV8m+6IUve+LDZndru41jlT1mT9g6C9krtsXesz3WZ5J9Z7/YCfvj/fB+e6fe2bJ1xWtnHrF/4J1fALhdrnQ=</latexit>
!m
!
!c!L
 < !m
= !m<latexit sha1_base64="x8cNt3LFkL1HiM2Pwztsc8sUnxc=">AAACGnicbVBNS8NAEN34WeNX1aOXxSJ4kJJEQS+CVEGPKlaFJpTNdlqX7iZhdyKW0N/hxb/ixYMi3sSL/8Zt7cGvBwOP92ZmZ1+cSWHQ8z6csfGJyanp0ow7Oze/sFheWr4waa451HkqU30VMwNSJFBHgRKuMg1MxRIu4+7BwL+8AW1EmpxjL4NIsU4i2oIztFKz7IcItzjc0zg7qkVFEHibQRDY2u4XbngIEhndo2GqoMOayu03yxWv6g1B/xJ/RCpkhJNm+S1spTxXkCCXzJiG72UYFUyj4BL6bpgbyBjvsg40LE2YAhMVw5P6dN0qLdpOta0E6VD9PlEwZUxPxbZTMbw2v72B+J/XyLG9GxUiyXKEhH891M4lxZQOcqItoYGj7FnCuBb2VsqvmWYcbZquDcH//eW/5CKo+lvV4HS7sl8bxVEiq2SNbBCf7JB9ckxOSJ1wckceyBN5du6dR+fFef1qHXNGMyvkB5z3T0JVnn4=</latexit>
C =
g2
 ¯n
> 1
<latexit sha1_base64="KanYr5/IQZhln3FSGDfS2rj1ERs=">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</latexit>
 > !m<latexit sha1_base64="Rh+OFI2sCJh9coK4HahUL0kuuWw=">AAACGHicbVA9T+NAEF1zwAXzFY6SxiJCokDBNpG4CiEooAyIAFJsRePNJKyya1u7Y0Rk5Wdcc3+FhoLTiZaOf8MmpODrSSM9vTczO/uSXApDvv/izPyYnZv/WVlwF5eWV1ara78uTVZoji2eyUxfJ2BQihRbJEjida4RVCLxKhkcj/2rW9RGZOkFDXOMFfRT0RMcyEqd6m5EeEeTPe3zk6O4DEN/JwxDW41R6UYDyHM4iDKFfegod9Sp1vy6P4H3lQRTUmNTNDvV56ib8UJhSlyCMe3AzykuQZPgEkduVBjMgQ+gj21LU1Bo4nJy0MjbskrX62XaVkreRH0/UYIyZqgS26mAbsxnbyx+57UL6v2OS5HmBWHK3x7qFdKjzBun5HWFRk5yaAlwLeytHr8BDZxslq4NIfj85a/kMqwHe/XwrFE7PJrGUWEbbJNts4Dts0N2ypqsxTj7w+7ZI/vn/HUenP/O01vrjDOdWWcf4Dy/ArTYnk4=</latexit>
ground state cooling

11. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Hybrid systems can cool motion in regimes where
optomechanics fails.
11
C. Genes et al., PRA 80, 061803 (2009)
A. Dantan et al., PRA 90, 033820 (2014)

12. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
We focus on membranes doped with two-level systems or
patterned with gratings.
12
H= !cc†
c + !mb†
b + g0c†
c(b + b†
)
+!aa†
a + [ + µ0(b + b†
)](a†
c + c†
a)<latexit sha1_base64="AkN8r++Ou/WrTyYD/Hu8Za5AjQI=">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</latexit>
H= cc†
c + !mb†
b + (˜g⇤
c + ˜gc†
)(b + b†
)
+ aa†
a + (a†
c + c†
a) + µ(a + a†
)(b + b†
)<latexit sha1_base64="y5VMsGYuU8J1DUaghYWCJKxuGKM=">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</latexit>
˜g = g0↵
i µ
+ i a
, µ = µ0↵
<latexit sha1_base64="jbiiho5jDa64J7+6H4B+5e9z2QE=">AAACW3icbVFRa9RAEN6kas9Y7VXxyZfFQxCsRxIL9kUoVdDHKl5buA1hstnklu4m6e5EPJb8SZ/0wb8i7l1P0NaBWT6+mW9n59uiU9JiHP8Iwq1bt+9sj+5G93buP9gd7z08tW1vuJjxVrXmvAArlGzEDCUqcd4ZAbpQ4qy4eLuqn30Rxsq2+YzLTmQa6kZWkgN6Kh8bhuIrru+Zf3p/nLk0jffTNPV5MLiIoVSlcPVA39A6jxmobgEvWWWAO8mUn1MC0/3gWA1awwvJ3gmFkMOwzy4veyh90Uv9+UccDfl4Ek/jddCbINmACdnEST7+xsqW91o0yBVYO0/iDjMHBiVXYohYb0UH/AJqMfewAS1s5tY7DfSZZ0patcZng3TN/q1woK1d6sJ3asCFvV5bkf+rzXusDjMnm65H0fCrQVWvKLZ0ZTQtpREc1dID4Eb6t1K+AG8c+u+IvAnJ9ZVvgtN0mryaph8PJkfHGztG5Al5Sp6ThLwmR+QDOSEzwsl38ivYDkbBz3ArjMKdq9Yw2GgekX8ifPwbw2+zvA==</latexit>
Basic Hamiltonian:
Linearization:
OC, C. Genes, A. Dantan, QST 4, 024002 (2019)ˇ

13. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Interference between interactions leads to a Fano
resonance in the cavity spectrum.
13
cavity noise
dopant noise
total noise
˙q= !mp,
˙p= !mq mp + ⇠ F,
F= ˜g⇤
c + ˜gc†
+ µ(a + a†
)<latexit sha1_base64="GyfMRpqikEG322zPu1LtSK4LIxQ=">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</latexit>
this work
no radiation pressure,
A. Dantan et al., PRA 90, 033820 (2014)
atoms in the cavity,
C. Genes et al., PRA 80, 061803 (2009)
g = 0<latexit sha1_base64="W5dhKlWsINsoq2jNbu6JXDbHvG4=">AAACDnicbVC7SgNBFJ31GddX1NJmMAQsJOyuAW2EEAsto5gHJEuYncwmQ2YfzNwVw7JfYOOv2FgoYmtt5984eRSaeODC4Zx779w5Xiy4Asv6NpaWV1bX1nMb5ubW9s5ufm+/oaJEUlankYhkyyOKCR6yOnAQrBVLRgJPsKY3vBz7zXsmFY/COxjFzA1IP+Q+pwS01M0XO8AeYLKnfXtVdVPHsU4cx9FVzlKzjy+wZWbdfMEqWRPgRWLPSAHNUOvmvzq9iCYBC4EKolTbtmJwUyKBU8Eys5MoFhM6JH3W1jQkAVNuOjkjw0Wt9LAfSV0h4In6eyIlgVKjwNOdAYGBmvfG4n9eOwH/3E15GCfAQjp9yE8EhgiPs8E9LhkFMdKEUMn1rZgOiCQUdIKmDsGe//IiaTgl+7Tk3JQLleosjhw6REfoGNnoDFXQNaqhOqLoET2jV/RmPBkvxrvxMW1dMmYzB+gPjM8feC6ZJg==</latexit>
µ = 0<latexit sha1_base64="E765DVRLRtAq3w+oCdFrD4JP0PQ=">AAACEHicbVC7SgNBFJ31GdfXqqXNYBAtJOyuAW2EEAsto5gHJEuYnUySIbMPZu6KYckn2PgrNhaK2Fra+TdONik08cCFwzn33rlz/FhwBbb9bSwsLi2vrObWzPWNza1ta2e3pqJEUlalkYhkwyeKCR6yKnAQrBFLRgJfsLo/uBz79XsmFY/COxjGzAtIL+RdTgloqW0dtYA9QLaneXtV9lLXtU9c19VVHKVmK0jwBbbNUdvK2wU7A54nzpTk0RSVtvXV6kQ0CVgIVBClmo4dg5cSCZwKNjJbiWIxoQPSY01NQxIw5aXZISN8qJUO7kZSVwg4U39PpCRQahj4ujMg0Fez3lj8z2sm0D33Uh7GCbCQTh7qJgJDhMfp4A6XjIIYakKo5PpWTPtEEgo6Q1OH4Mx+eZ7U3IJzWnBvivlSeRpHDu2jA3SMHHSGSugaVVAVUfSIntErejOejBfj3fiYtC4Y05k99AfG5w8hw5oR</latexit>
OC, C. Genes, A. Dantan, QST 4, 024002 (2019)ˇ

14. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
With strong coupling, the membrane can be used as an
end mirror.
14
Frequency
Transmission
Standard cavity
Hybrid mirror
OC, A. Dantan, C. Genes, PRL 122, 243601 (2019)ˇ

15. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
The membrane’s internal dynamics has to be included in
the Langevin equations.
15
c<latexit sha1_base64="e/ZnXwNWuGO9QYPMKK3xK/UoST4=">AAACCnicbVC7SgNBFJ2Nr7i+Vi1tRoNgIWF3DWgZYqFlFPOAZAmzk0kyZPbBzF0xLKlt/BUbC0Vs/QI7/8bJJoUmHrhwOOfeO3eOHwuuwLa/jdzS8srqWn7d3Njc2t6xdvfqKkokZTUaiUg2faKY4CGrAQfBmrFkJPAFa/jDy4nfuGdS8Si8g1HMvID0Q97jlICWOtZhG9gDZHtat1cVL3Vd+9R1XV2lcWpSc9yxCnbRzoAXiTMjBTRDtWN9tbsRTQIWAhVEqZZjx+ClRAKngo3NdqJYTOiQ9FlL05AETHlpdsIYH2uli3uR1BUCztTfEykJlBoFvu4MCAzUvDcR//NaCfQuvJSHcQIspNOHeonAEOFJLrjLJaMgRpoQKrm+FdMBkYSCTs/UITjzX14kdbfonBXdm1KhXJnFkUcH6AidIAedozK6RlVUQxQ9omf0it6MJ+PFeDc+pq05Yzazj/7A+PwBrRSYTQ==</latexit>
d<latexit sha1_base64="BlgRZ0e/sz/MukfcjDDvlpzjS8w=">AAACCnicbVC7TsMwFHXKq4RXgJElUCExoCoJlWCsygBjQfQhtVHluG5r1XEi+wZRRZ1Z+BUWBhBi5QvY+BvctAO0HOlKR+fce319gpgzBY7zbeSWlldW1/Lr5sbm1vaOtbtXV1EiCa2RiEeyGWBFORO0Bgw4bcaS4jDgtBEMLyd+455KxSJxB6OY+iHuC9ZjBIOWOtZhG+gDZHtat1cVP/U859TzPF2lcWp2zXHHKjhFJ4O9SNwZKaAZqh3rq92NSBJSAYRjpVquE4OfYgmMcDo224miMSZD3KctTQUOqfLT7ISxfayVrt2LpC4Bdqb+nkhxqNQoDHRniGGg5r2J+J/XSqB34adMxAlQQaYP9RJuQ2RPcrG7TFICfKQJJpLpW20ywBIT0OmZOgR3/suLpO4V3bOid1MqlCuzOPLoAB2hE+Sic1RG16iKaoigR/SMXtGb8WS8GO/Gx7Q1Z8xm9tEfGJ8/rpqYTg==</latexit>
bin<latexit sha1_base64="IJYl7h6e7GyW+HtWYRaoBKZgphI=">AAACFnicbVDLSsNAFJ3UV42vqks3wSK40JLEgi5LXeiyin1AGspkOm2HTh7M3Igl5Cvc+CtuXCjiVtz5N07TLLT1wIXDOffO3Hu8iDMJpvmtFZaWV1bXiuv6xubW9k5pd68lw1gQ2iQhD0XHw5JyFtAmMOC0EwmKfY/Ttje+nPrteyokC4M7mETU9fEwYANGMCipVzrtAn2A7B3n9qruJrZtnti2raqaJrrX6/oYRsJPWJDqaa9UNitmBmORWDkpoxyNXumr2w9J7NMACMdSOpYZgZtgAYxwmurdWNIIkzEeUkfRAPtUukm2TmocKaVvDEKhKgAjU39PJNiXcuJ7qnO6pJz3puJ/nhPD4MJVF0Ux0IDMPhrE3IDQmGZk9JmgBPhEEUwEU7saZIQFJqCS1FUI1vzJi6RlV6yzin1TLdfqeRxFdIAO0TGy0DmqoWvUQE1E0CN6Rq/oTXvSXrR37WPWWtDymX30B9rnD7cTndc=</latexit>
cin<latexit sha1_base64="u0JxZb1/IoHLU/PeUHEqFaJhe3A=">AAACFnicbVDLSsNAFJ3UV42vqks3wSK40JLEgi5LXeiyin1AGspkOm2HTh7M3Igl5Cvc+CtuXCjiVtz5N07TLLT1wIXDOffO3Hu8iDMJpvmtFZaWV1bXiuv6xubW9k5pd68lw1gQ2iQhD0XHw5JyFtAmMOC0EwmKfY/Ttje+nPrteyokC4M7mETU9fEwYANGMCipVzrtAn2A7B3n9qruJrZtnti2raqaJjrpdX0MI+EnLEj1tFcqmxUzg7FIrJyUUY5Gr/TV7Yck9mkAhGMpHcuMwE2wAEY4TfVuLGmEyRgPqaNogH0q3SRbJzWOlNI3BqFQFYCRqb8nEuxLOfE91TldUs57U/E/z4lhcOGqi6IYaEBmHw1ibkBoTDMy+kxQAnyiCCaCqV0NMsICE1BJ6ioEa/7kRdKyK9ZZxb6plmv1PI4iOkCH6BhZ6BzV0DVqoCYi6BE9o1f0pj1pL9q79jFrLWj5zD76A+3zB7ilndg=</latexit>
˙c= ( + i!c)c (
p
L + i )d +
p
2Lbin +
p
2Rcin,
˙d= ( + i!d)d (
p
L + i )c +
p
2 bin<latexit sha1_base64="T3RS3Qwm58CO3oQSsZq5TWg4Rjk=">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</latexit>
bout= bin
p
2Lc
p
2 d,
cout= cin
p
2Rc<latexit sha1_base64="IkBpW0RpafRn5YLebZygtBjQyRQ=">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</latexit>

16. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
System parameters can be extracted from comparison to
classical calculations.
16
Langevin equations
A. Naesby, A. Dantan, Opt. Exp. 26, 29886 (2018)
Transfer matrix calculation
Frequency-independent reflection
OC, A. Dantan, C. Genes, PRL 122, 243601 (2019)ˇ
linewidth reduction factor
FSR<latexit sha1_base64="Idhq8097aEt+5yVAhKmSEUY1KT8=">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</latexit>

17. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
The Fano resonance suppresses Stokes scattering in
cooling.
17
pump
anti-Stokes
Stokes
sam
e
reflectivity
sam
e
linew
idth
hybrid
cavity
¯n = 100
¯n = 10

18. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Many systems can be used to achieve these effects.
18
Photonic crystal membranes
R. Norte et al., PRL 116, 147202 (2016)
E. Shahmoon et al., arXiv:1810.01052
Trapped atom arrays
Excitons in semiconductors
G. Scuri et al., PRL 120, 037402 (2018)
P. Back et al., PRL 120, 037401 (2018)
Atoms trapped along waveguides
Mirhosseini et al., Nature 569, 692 (2019)

19. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
The approach can have other applications in
optomechanics and cavity QED.
19
• Strong amplification and limit cycles
• Enhanced emission into the zero-phonon line
E.V. Denning, J. Iles-Smith, J. Mork, arXiv:1907.13423
• Pulsed lasing
Y. Yu et al., Nat. Photon. 11, 81 (2017)
• High-fidelity state transfer

20. Optical levitation with coherent scattering
Radim Filip
Palacký University
OC, R. Filip, arXiv:1908:07230ˇ

21. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Optical levitation allows for high-quality mechanical
motion without damping.
21
Nonspherical particles
S. Kuhn et al., Optica 4, 356 (2017)
Hybrid systems
L.P. Neukirch et al., Nat. Photon. 9, 653 (2015)
Cavity optomechanics
N. Kiesel, PNAS 110, 14180 (2013)
Thermodynamics
I.A. Martinez et al., Nat. Phys. 12, 67 (2016)

22. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Coherent scattering is a new tool for optomechanical
interactions.
22
U. Delic et al., PRL 122, 123602 (2019)
D. Windey et al., PRL 122, 123601 (2019)

23. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
The system is versatile, allowing one-, two-, and three-
dimensional coupling.
23
Hint/ Ecav(r) · Etw(r)
⇡ ( xx + yy)(c + c†
) i zz(c c†
)<latexit sha1_base64="B/AKfXv6gZgMHGG+4IPGW70SjBU=">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</latexit>
C. Gonzalez-Ballestero et al., PRA 100, 013805 (2019)
Intracavity intensity
Radial coupling
Axial coupling
Polarization
Etw<latexit sha1_base64="bRQQNOEkJg9znsC3zqgs56MYHpg=">AAACH3icbVDLSsNAFJ3UV42vqks3wSK4kJLEoi5LRXRZxT6gDWUynbRDJw9mbtQS8idu/BU3LhQRd/0bp2kX2nrgwuHcx5w5bsSZBNMca7ml5ZXVtfy6vrG5tb1T2N1ryDAWhNZJyEPRcrGknAW0Dgw4bUWCYt/ltOkOLyf95gMVkoXBPYwi6vi4HzCPEQxK6hbOOkCfILvTvruuOoltmye2basqp4ne8TEMXC+5SrsZFX4Cj6medgtFs2RmMBaJNSNFNEOtW/ju9EIS+zQAwrGUbcuMwEmwAEY4TfVOLGmEyRD3aVvRAPtUOknmKzWOlNIzvFCoCsDI1N8bCfalHPmumpyYlPO9ifhfrx2Dd+EkLIhioAGZPuTF3IDQmIRl9JigBPhIEUwEU14NMsACE1CR6ioEa/7Li6Rhl6zTkn1bLlaqszjy6AAdomNkoXNUQTeohuqIoGf0it7Rh/aivWmf2td0NKfNdvbRH2jjH0y5oe4=</latexit>
Ecav<latexit sha1_base64="nvRiBR5yCYIOD0X3nzXvyGTc6/c=">AAACIHicbVDLSsNAFJ3UV42vqks3wSK4kJLEQl2Wiuiyin1AG8pkOmmHTh7M3BRLyKe48VfcuFBEd/o1TtMutPXAhcO5jzlz3IgzCab5peVWVtfWN/Kb+tb2zu5eYf+gKcNYENogIQ9F28WSchbQBjDgtB0Jin2X05Y7upz2W2MqJAuDe5hE1PHxIGAeIxiU1CtUukAfILvTubuuOYltm2e2basqp4ne9TEMXS+5SnsZFX5C8DjV016haJbMDMYyseakiOao9wqf3X5IYp8GQDiWsmOZETgJFsAIp6nejSWNMBnhAe0oGmCfSifJjKXGiVL6hhcKVQEYmfp7I8G+lBPfVZNTl3KxNxX/63Vi8C6chAVRDDQgs4e8mBsQGtO0jD4TlACfKIKJYMqrQYZYYAIqU12FYC1+eZk07ZJ1XrJvy8VqbR5HHh2hY3SKLFRBVXSD6qiBCHpEz+gVvWlP2ov2rn3MRnPafOcQ/YH2/QP8tqJH</latexit>

24. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
We are interested in generating one-mode mechanical
squeezing.
24
H =
!m
2
(x2
+ p2
) + c†
c (c + c†
)x
<latexit sha1_base64="tmpBmTUn3auc6X1jLep9ed+hzB0=">AAACUXicbVFLixNBEO6Mr3XWR9Sjl8YgZImGmXZBL8KyCu5xFbO7kJmEmp6aSbM9D7prJGGYv+hBT/4PLx4UO9kgumtBwcf31aPr66TWylIQfOt5167fuHlr57a/e+fuvfv9Bw9PbNUYiRNZ6cqcJWBRqxInpEjjWW0QikTjaXL+Zq2ffkJjVVV+pFWNcQF5qTIlgRw17y8iwiVt5kw/vDuMWyGCZ0IIl/td6x/x1zzKDMg2qgrMYV50reiGy5kY1TOxN4reoibgchalkOdouHweabc9haEc/WH3ln437w+CcbAJfhWEWzBg2zie979EaSWbAkuSGqydhkFNcQuGlNTY+VFjsQZ5DjlOHSyhQBu3m0s6/tQxKc8q47IkvmH/7mihsHZVJK6yAFrYy9qa/J82bSh7FbeqrBvCUl4syhrNqeJre3mqDErSKwdAGuXeyuUCnIHkPsF3JoSXT74KTsQ4fDEW7/cHB4dbO3bYY/aEDVnIXrIDdsSO2YRJ9pl9Zz/Zr97X3g+Ped5Fqdfb9jxi/4S3+xtPKLCq</latexit>
˙c= ( + i )c + i x +
p
2cin
˙x= !mp
˙p !mx p + (c + c†
) + ⇠<latexit sha1_base64="YAQ9sJ5I2a9n+Mi7hWjhyiIy2vE=">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</latexit>

25. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
First, the cavity can be adiabatically eliminated from the
dynamics.
25
˙x= (!e↵ + ⇣e↵ )p,
˙p= (!e↵ ⇣e↵ )x p + noise<latexit sha1_base64="ha6WZ22dQ3afGOrXqOE1z/jgdCU=">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</latexit>
⌘ =
Vsq
Vasq<latexit sha1_base64="fHk0fk7TZEP2Er3C1iIntlG4y04=">AAACNHicbVDJSsRAEO24G7dRj14aB8GDDEkU9CKIHhS8qDijMAlDp6eijZ3F7oo4hHyUFz/EiwgeFPHqN9gZ5+BWUPDq1dKvX5hJodFxnqyh4ZHRsfGJSXtqemZ2rja/0NJprjg0eSpTdR4yDVIk0ESBEs4zBSwOJZyFV3tV/+wGlBZpcoq9DIKYXSQiEpyhoTq1Qx/hFvt32if7u0Hhec6a53kmN8rC9gEZ3aZ+pBgvWh0/Znip4kJfl+W3klW1XXZqdafh9IP+Be4A1Mkgjjq1B7+b8jyGBLlkWrddJ8OgYAoFl1Dafq4hY/yKXUDbwITFoIOiL7akK4bp0ihVJhOkffb7RsFirXtxaCYrmfp3ryL/67VzjLaCQiRZjpDwr4eiXFJMaeUg7QoFHGXPAMaVMFopv2TGIDQ+28YE9/eX/4KW13DXG97xRn1nd2DHBFkiy2SVuGST7JADckSahJM78kheyKt1bz1bb9b71+iQNdhZJD/C+vgEcWOq1g==</latexit>
Numbers from U. Delic et al., PRL 122, 123602 (2019)
!e↵ = !m
2
<latexit sha1_base64="2hw9EBUzqtKcRfKxw5m4izK4+mE=">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</latexit>
⇣e↵ =
2
<latexit sha1_base64="X9qgJEyDh80ClmWqsjd1JZ8KU40=">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</latexit>

26. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Stronger squeezing can be generated with a modulated
trapping beam.
26
E(t) = E0[1 + ↵ cos(2!mt + )]<latexit sha1_base64="WoTFMZfaxpnyLfbFIpyA7RESYn0=">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</latexit>
2!mt + )]2
x2
+ c†
c [1 + ↵ cos(2!mt + )]x(c + c†
)
H =
!m
2
p2
+
!m
2
[1 + ↵ cos(2!mt + )]2
x2
+ c†
c [1 + ↵ cos(2!mt +
<latexit sha1_base64="z4Ykhr7XosZvqSNdQL/Oogp145Y=">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</latexit>
tweezer amplitude

27. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Stronger squeezing can be generated with a modulated
trapping beam.
27
˙x = !e↵ p ⇣e↵ (x sin + p cos ) + noise<latexit sha1_base64="9Y1BQ8JvlH+cmemx5r6v81q25co=">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</latexit>
˙p = !e↵ x ⇣e↵ (x cos p sin ) + noise<latexit sha1_base64="E51O41QkBGpeSHVIvtBDwd9dPPI=">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</latexit>
!e↵<latexit sha1_base64="4xz0xpwwfGb9IrAurwC+5rLGJUs=">AAAB/HicbVDLSsNAFJ34rPUV7dJNsAiuSlIFXRbduKxgH9CEMpnetENnJmFmIoRQf8WNC0Xc+iHu/BsnbRbaemDgcM693DMnTBhV2nW/rbX1jc2t7cpOdXdv/+DQPjruqjiVBDokZrHsh1gBowI6mmoG/UQC5iGDXji9LfzeI0hFY/GgswQCjseCRpRgbaShXfNjDmM89DnWE8lziKLZ0K67DXcOZ5V4JamjEu2h/eWPYpJyEJowrNTAcxMd5FhqShjMqn6qIMFkiscwMFRgDirI5+FnzplRRk4US/OEdubq740cc6UyHprJIqNa9grxP2+Q6ug6yKlIUg2CLA5FKXN07BRNOCMqgWiWGYKJpCarQyZYYqJNX1VTgrf85VXSbTa8i0bz/rLeuinrqKATdIrOkYeuUAvdoTbqIIIy9Ixe0Zv1ZL1Y79bHYnTNKndq6A+szx9jAZU/</latexit>
⇣e↵<latexit sha1_base64="f7DKz42CBtk8xEsxJCY6T/O0OX0=">AAAB+3icbVDLSsNAFJ3UV62vWJdugkVwVZIq6LLoxmUF+4AmhMn0ph06mYSZiVhDfsWNC0Xc+iPu/BsnbRbaemDgcM693DMnSBiVyra/jcra+sbmVnW7trO7t39gHtZ7Mk4FgS6JWSwGAZbAKIeuoorBIBGAo4BBP5jeFH7/AYSkMb9XswS8CI85DSnBSku+WXefQGHfjbCaiCiDMMx9s2E37TmsVeKUpIFKdHzzyx3FJI2AK8KwlEPHTpSXYaEoYZDX3FRCgskUj2GoKccRSC+bZ8+tU62MrDAW+nFlzdXfGxmOpJxFgZ4sMsplrxD/84apCq+8jPIkVcDJ4lCYMkvFVlGENaICiGIzTTARVGe1yAQLTJSuq6ZLcJa/vEp6raZz3mzdXTTa12UdVXSMTtAZctAlaqNb1EFdRNAjekav6M3IjRfj3fhYjFaMcucI/YHx+QO2xJTg</latexit>
= 0<latexit sha1_base64="w1xJ/c3CF++n8TidbOg4yITMbes=">AAAB73icbVBNS8NAEJ34WetX1aOXxSJ4KkkV9CIUvXisYD+gDWWz3bRLN5u4OxFK6J/w4kERr/4db/4bt20O2vpg4PHeDDPzgkQKg6777aysrq1vbBa2its7u3v7pYPDpolTzXiDxTLW7YAaLoXiDRQoeTvRnEaB5K1gdDv1W09cGxGrBxwn3I/oQIlQMIpWaneToSDXxO2Vym7FnYEsEy8nZchR75W+uv2YpRFXyCQ1puO5CfoZ1SiY5JNiNzU8oWxEB7xjqaIRN342u3dCTq3SJ2GsbSkkM/X3REYjY8ZRYDsjikOz6E3F/7xOiuGVnwmVpMgVmy8KU0kwJtPnSV9ozlCOLaFMC3srYUOqKUMbUdGG4C2+vEya1Yp3XqneX5RrN3kcBTiGEzgDDy6hBndQhwYwkPAMr/DmPDovzrvzMW9dcfKZI/gD5/MHtjuPGA==</latexit>
= ⇡/2<latexit sha1_base64="D/GluAn2bRopIVcFvxBOUCyyt2Q=">AAAB83icbVBNSwMxEJ2tX7V+VT16CRbBU91tBb0IRS8eK9gP6C4lm2bb0Gw2JFmhLP0bXjwo4tU/481/Y9ruQVsfDDzem2FmXig508Z1v53C2vrG5lZxu7Szu7d/UD48auskVYS2SMIT1Q2xppwJ2jLMcNqViuI45LQTju9mfueJKs0S8WgmkgYxHgoWMYKNlXxfjhi6Qb5kF7V+ueJW3TnQKvFyUoEczX75yx8kJI2pMIRjrXueK02QYWUY4XRa8lNNJSZjPKQ9SwWOqQ6y+c1TdGaVAYoSZUsYNFd/T2Q41noSh7Yzxmakl72Z+J/XS010HWRMyNRQQRaLopQjk6BZAGjAFCWGTyzBRDF7KyIjrDAxNqaSDcFbfnmVtGtVr16tPVxWGrd5HEU4gVM4Bw+uoAH30IQWEJDwDK/w5qTOi/PufCxaC04+cwx/4Hz+AHT9kKY=</latexit>

28. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Steady-state squeezing can be generated dissipatively.
28
= !m<latexit sha1_base64="x8cNt3LFkL1HiM2Pwztsc8sUnxc=">AAACGnicbVBNS8NAEN34WeNX1aOXxSJ4kJJEQS+CVEGPKlaFJpTNdlqX7iZhdyKW0N/hxb/ixYMi3sSL/8Zt7cGvBwOP92ZmZ1+cSWHQ8z6csfGJyanp0ow7Oze/sFheWr4waa451HkqU30VMwNSJFBHgRKuMg1MxRIu4+7BwL+8AW1EmpxjL4NIsU4i2oIztFKz7IcItzjc0zg7qkVFEHibQRDY2u4XbngIEhndo2GqoMOayu03yxWv6g1B/xJ/RCpkhJNm+S1spTxXkCCXzJiG72UYFUyj4BL6bpgbyBjvsg40LE2YAhMVw5P6dN0qLdpOta0E6VD9PlEwZUxPxbZTMbw2v72B+J/XyLG9GxUiyXKEhH891M4lxZQOcqItoYGj7FnCuBb2VsqvmWYcbZquDcH//eW/5CKo+lvV4HS7sl8bxVEiq2SNbBCf7JB9ckxOSJ1wckceyBN5du6dR+fFef1qHXNGMyvkB5z3T0JVnn4=</latexit>
E(t) = E0[1 + ↵ cos(2!mt + )]<latexit sha1_base64="WoTFMZfaxpnyLfbFIpyA7RESYn0=">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</latexit>

29. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Steady-state squeezing can be generated dissipatively.
29
H =
!m↵
4
( 2
+ †2
↵ †
) e↵ ( c†
+ †
c)
<latexit sha1_base64="9oHNiNOy/6S2chvuMQZVgkTKT4I=">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</latexit>
=
1
p
4 ↵2
(2b + ↵b†
)
<latexit sha1_base64="eExlKz+gZY1Oe7f03ve4BkCKznM=">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</latexit>
e↵ =
r
4 ↵2
8<latexit sha1_base64="sq2aWzn6wY+KJluRO/q6L5rgc/I=">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</latexit>

30. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
Extensions and applications of this scheme are possible.
30
• Towards full control of motion of levitated particles
• Mechanical squeezing for force sensing
J. Gieseler et al., Nat. Phys. 9, 806 (2013)
• Parametric and dissipative two-mode squeezing
A. Pontin et al., PRL 116, 103601 (2016)
C.F. Ockeloen-Korppi et al., Nature 556, 478 (2018)

31. Ondrej Cernotík: Improved optomechanical interactions for quantum technologiesˇˇ @cernotik
New coupling mechanisms open new avenues for
optomechanical technologies.
31
• Coherent scattering for control of levitated particles
OC, R. Filip, arXiv:1908:07230ˇ
• Hybrid membranes for modified cavity response
OC, A. Dantan, C. Genes, PRL 122, 243601 (2019)ˇ
OC, C. Genes, A. Dantan, QST 4, 024002 (2019)ˇ