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Improved optomechanical interactions for quantum technologies

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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.

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Improved optomechanical interactions for quantum technologies

  1. 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. 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. 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. 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=">AAACNHicbVDLSgNBEJz17fqKevQyGARBCburoBchxIOCFxWjQnYJvZNJMjj7cKZXDEs+yosf4kUED4p49RucrDn4KmgoqrpnuitMpdDoOE/WyOjY+MTk1LQ9Mzs3v1BaXDrXSaYYr7NEJuoyBM2liHkdBUp+mSoOUSj5RXi1P/AvbrjSIonPsJfyIIJOLNqCARqpWTrykd9i8U7j9KAW5J7nbHqeZ2q7n9vgY0J9kGkX6AaFTf/6OoMW7TSdgdGhewUtfLvfLJWdilOA/iXukJTJEMfN0oPfSlgW8RiZBK0brpNikINCwSTv236meQrsCjq8YWgMEddBXizbp2tGadF2okzFSAv1+0QOkda9KDSdEWBX//YG4n9eI8P2bpCLOM2Qx+zro3YmqTl4kCBtCcUZyp4hwJQwu1LWBQUMTc62CcH9ffJfcu5V3K2Kd7JdrtaGcUyRFbJK1olLdkiVHJJjUieM3JFH8kJerXvr2Xqz3r9aR6zhzDL5AevjE65Rp9E=</latexit> Interaction Hamiltonian Hint = g0a† a(b + b† ) ! g(a + a† )(b + b† )<latexit sha1_base64="0MfHSOQNZXhzBE8bw9IHcH2lZU8=">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</latexit>
  5. 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. 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. 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. 8. Improved optomechanical interactions Optical levitation with coherent scattering Cavity optomechanics with hybrid membranes
  9. 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. 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=">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</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. 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. 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=">AAAC43icfVJLb9QwEHbCq4RHFzhysViBtgpaJaESXJCqcqDHgti2UhzCxPGmVu0k2A5iFeXKhQMIce2f6o2/wgnvNizbFnWkkT59M/PNw85qwbUJgl+Oe+Xqtes31m56t27fubs+uHd/T1eNomxCK1Gpgww0E7xkE8ONYAe1YiAzwfazo1fz+P4npjSvyndmVrNEQlHyKadgLJUOfhPDPpuFTvz29XbSRlHwNIoi65td6+10+MmlGS8xqSQrIKWYvic5FAVTmPo9KXG2JDO/SIOVnFHmL4MbHSHe5Y3IxwZy/FcYYCkEfkyEXTgHn8gmDc7oJiNYmepfd9jwunQwDMbBwvBFEPZgiHrbTQcnJK9oI1lpqACt4zCoTdKCMpwK1nmk0awGegQFiy0sQTKdtIuFOvzYMjmeVsp6afCCXa1oQWo9k5nNlGAO9fnYnPxfLG7M9EXS8rJuDCvpaaNpI7Cp8PzBcc4Vo0bMLACquJ0V00NQQI39Fp49Qnh+5YtgLxqHz8bRm83h1nZ/jjX0ED1CIxSi52gL7aBdNEHU+eB8cb45313mfnV/uD9PU12nr3mAzph7/Af4uOFj</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=">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</latexit> Basic Hamiltonian: Linearization: OC, C. Genes, A. Dantan, QST 4, 024002 (2019)ˇ
  13. 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. 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. 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. 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. 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. 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. 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. 20. Optical levitation with coherent scattering Radim Filip Palacký University OC, R. Filip, arXiv:1908:07230ˇ
  21. 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. 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. 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. 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=">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</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. 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=">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</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. 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. 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. 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. 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=">AAACkXicbVFNb9QwEHXCVwnQLvTIxWKF1Kp0lYSVaA9Fq3KgEpeC2LbSOkSOM8latZPIdhArK/+H38ONf4M3GyTaMtLIz2/ejMczWSO4NmH42/Pv3X/w8NHW4+DJ02fbO6PnLy503SoGc1aLWl1lVIPgFcwNNwKuGgVUZgIus+sP6/jld1Ca19VXs2ogkbSseMEZNY5KRz+JgR+mr7P48vE0sXEcvonj2Pm0s8EZPsGkUJRZUksoaSoJFc2Sdnba7ZEMDP0WH2xOS3JalqBw3B1uRBt+oPvLPj4kwjWX05RIapZKWiiKoRJmf7X44EYqZvtBl47G4STsDd8F0QDGaLDzdPSL5DVrJVSGCar1Igobk1iqDGcCuoC0GhrKrmkJCwcrKkEntp9Eh187JsdFrZxXBvfsvxmWSq1XMnPK9T/07dia/F9s0ZriKLG8aloDFds8VLQCmxqv14NzroAZsXKAMsVdr5gtqVuAcUsM3BCi21++Cy7iSfR2En+ejmenwzi20Ev0Cu2hCL1DM3SGztEcMW/bm3on3nt/1z/2Z/6g9b0hZxfdMP/TH87nxgs=</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=">AAACQnicbVDLThRBFK1GRGwEB126qTghcaGT7mYS2ZAQWOASiAOY6XZyu+Y2U6H6YdVt46TS38aGL3DnB7hxoSFsXVgz9AKBk9zk5Nz3SSslDQXBD2/h0eLjpSfLT/2VZ6trzzvrL45NWWuBA1GqUp+mYFDJAgckSeFppRHyVOFJer43y598RW1kWXykaYVJDmeFzKQActKo8ykm/EbzOcOj/d3ERlHwNooiF/3G+rFyo8YwinOgic4tZlnDt3krx+aLJhtnGoTtv4tBVRP4HDV2q2n8ZtTpBr1gDn6fhC3pshYHo873eFyKOseChAJjhmFQUWJBkxQKGz+uDVYgzuEMh44WkKNJ7Pz0hm84ZcyzUrsoiM/V2x0WcmOmeeoqZ6+Yu7mZ+FBuWFO2lVhZVDVhIW4WZbXiVPKZn3wsNQpSU0dAaOlu5WICzhFyrvvOhPDuy/fJcdQLN3vRYb+7s9vascxesdfsDQvZe7bDPrADNmCCXbCf7Df74116v7wr7/qmdMFre16y/+D9/Qc2FbAP</latexit>
  30. 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. 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

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