We propose a scheme for enhancing the optomechanical coupling between microwave and mechanical resonators by up to seven orders of magnitude to the ultrastrong coupling limit in a circuit optomechanical setting. The tripartite system considered here consists of a Josephson junction Cooper-pair box that mediates the coupling between the microwave cavity and the mechanical resonator. The optomechanical coupling can be modified by tuning the gate charge and the magnetic flux bias of the Cooper-pair box which in turn affect the Josephson capacitance of the Cooper-pair box. We additionally show that with a suitable choice of tuning parameters, the optomechanical coupling vanishes and the system purely exhibits a cross-Kerr type of nonlinearity between the cavity and the mechanical resonator. This allows the system to be used for phonon counting.We propose a scheme for enhancing the optomechanical coupling between microwave and mechanical resonators by up to seven orders of magnitude to the ultrastrong coupling limit in a circuit optomechanical setting. The tripartite system considered here consists of a Josephson junction Cooper-pair box that mediates the coupling between the microwave cavity and the mechanical resonator. The optomechanical coupling can be modified by tuning the gate charge and the magnetic flux bias of the Cooper-pair box which in turn affect the Josephson capacitance of the Cooper-pair box. We additionally show that with a suitable choice of tuning parameters, the optomechanical coupling vanishes and the system purely exhibits a cross-Kerr type of nonlinearity between the cavity and the mechanical resonator. This allows the system to be used for phonon counting.

Physical review. B./Physical review. BApr 25, 202216 citations

Enhancing Optomechanical Coupling via the Josephson Effect

Tero Tapio Heikkilä, Francesco Massel, Jani Tuorila +2 more

Cavity optomechanics is showing promise for studying quantum mechanics in large systems. However, the smallness of the radiation-pressure coupling is a serious hindrance. Here we show how the charge tuning of the Josephson inductance in a single-Cooper-pair transistor can be exploited to arrange a strong radiation-pressure-type coupling ${g}_{0}$ between mechanical and microwave resonators. In a certain limit of parameters, such a coupling can also be seen as a qubit-mediated coupling of two resonators. We show that this scheme allows reaching extremely high ${g}_{0}$ . Contrary to the recent proposals for exploiting the nonlinearity of a large radiation-pressure coupling, the main nonlinearity in this setup originates from a cross-Kerr type of coupling between the resonators, where the cavity refractive index depends on the phonon number. The presence of this coupling will allow accessing the individual phonon numbers via the measurement of the cavity.Cavity optomechanics is showing promise for studying quantum mechanics in large systems. However, the smallness of the radiation-pressure coupling is a serious hindrance. Here we show how the charge tuning of the Josephson inductance in a single-Cooper-pair transistor can be exploited to arrange a strong radiation-pressure-type coupling ${g}_{0}$ between mechanical and microwave resonators. In a certain limit of parameters, such a coupling can also be seen as a qubit-mediated coupling of two resonators. We show that this scheme allows reaching extremely high ${g}_{0}$. Contrary to the recent proposals for exploiting the nonlinearity of a large radiation-pressure coupling, the main nonlinearity in this setup originates from a cross-Kerr type of coupling between the resonators, where the cavity refractive index depends on the phonon number. The presence of this coupling will allow accessing the individual phonon numbers via the measurement of the cavity.

arXiv:1311.3802Physical Review LettersMay 23, 2014136 citations

Improving photon blockade, entanglement, and mechanical-cat-state generation in a generalized cross-Kerr optomechanical circuit

H. Solki, Ali Motazedifard, M. H. Naderi

We propose a feasible experimental scheme to improve the few-photon optomechanical effects, including photon blockade and mechanical-Schr\"odinger-cat-state generation, as well as photon-phonon entanglement in a tripartite microwave-optomechanical circuit. The system under consideration is formed by a single-Cooper-pair transistor, a microwave $LC$ resonator, and a micromechanical resonator. Our scheme is based on an additional higher-order (generalized) nonlinear cross-Kerr type of coupling, linearly dependent on photon number while quadratically dependent on mechanical phonon number, which can be realized via adjusting the gate charge of the Cooper-pair transistor. We show, both analytically and numerically, that the presence of both cross-Kerr and generalized cross-Kerr nonlinearities not only may give rise to the enhancement of one- and two-photon blockades as well as photon-induced tunneling but can also provide more controllability over them. Furthermore, it is shown that in the regime of zero optomechanical coupling, with the aid of generalized cross-Kerr nonlinearity, one can generate multicomponent mechanical superposition states which exhibit robustness against system dissipations. We also study the steady-state entanglement between the microwave and mechanical modes, the results of which signify the role of generalized cross-Kerr nonlinearity in enhancing the entanglement in the regime of large red detuning. The proposed generalized cross-Kerr optomechanical system can find potential applications in microwave quantum sensing, quantum telecommunication, and quantum information protocols.We propose a feasible experimental scheme to improve the few-photon optomechanical effects, including photon blockade and mechanical-Schr\"odinger-cat-state generation, as well as photon-phonon entanglement in a tripartite microwave-optomechanical circuit. The system under consideration is formed by a single-Cooper-pair transistor, a microwave $LC$ resonator, and a micromechanical resonator. Our scheme is based on an additional higher-order (generalized) nonlinear cross-Kerr type of coupling, linearly dependent on photon number while quadratically dependent on mechanical phonon number, which can be realized via adjusting the gate charge of the Cooper-pair transistor. We show, both analytically and numerically, that the presence of both cross-Kerr and generalized cross-Kerr nonlinearities not only may give rise to the enhancement of one- and two-photon blockades as well as photon-induced tunneling but can also provide more controllability over them. Furthermore, it is shown that in the regime of zero optomechanical coupling, with the aid of generalized cross-Kerr nonlinearity, one can generate multicomponent mechanical superposition states which exhibit robustness against system dissipations. We also study the steady-state entanglement between the microwave and mechanical modes, the results of which signify the role of generalized cross-Kerr nonlinearity in enhancing the entanglement in the regime of large red detuning. The proposed generalized cross-Kerr optomechanical system can find potential applications in microwave quantum sensing, quantum telecommunication, and quantum information protocols.

arXiv:2310.02443Physical Review ADec 6, 202318 citations

Strong and tunable couplings in flux-mediated optomechanics

Olga Shevchuk, Gary Alexander Steele, Yaroslav M. Blanter

We investigate a superconducting interference device (SQUID) with two asymmetric Josephson junctions coupled to a mechanical resonator embedded in the loop of the SQUID. We quantize this system in the case when the frequency of the mechanical resonator is much lower than the cavity frequency of the SQUID and in the case when they are comparable. In the first case, the radiation pressure and the cross-Kerr type interactions arise and are modified by the asymmetry. The cross-Kerr type coupling is the leading term at the extremum points where the radiation pressure is zero. In the second case, the main interaction is the single-photon beam splitter, which exists only at a finite asymmetry. Another interaction in this regime is of cross-Kerr type, which exists at all asymmetries, but is generally much weaker than the beam splitter interaction. Increasing magnetic field can substantially enhance the optomechanical couplings strength with a potential for the radiation pressure coupling to reach the single-photon strong coupling regime, even the ultrastrong coupling regime, in which the single-photon coupling rate exceeds the mechanical frequency.We investigate a superconducting interference device (SQUID) with two asymmetric Josephson junctions coupled to a mechanical resonator embedded in the loop of the SQUID. We quantize this system in the case when the frequency of the mechanical resonator is much lower than the cavity frequency of the SQUID and in the case when they are comparable. In the first case, the radiation pressure and the cross-Kerr type interactions arise and are modified by the asymmetry. The cross-Kerr type coupling is the leading term at the extremum points where the radiation pressure is zero. In the second case, the main interaction is the single-photon beam splitter, which exists only at a finite asymmetry. Another interaction in this regime is of cross-Kerr type, which exists at all asymmetries, but is generally much weaker than the beam splitter interaction. Increasing magnetic field can substantially enhance the optomechanical couplings strength with a potential for the radiation pressure coupling to reach the single-photon strong coupling regime, even the ultrastrong coupling regime, in which the single-photon coupling rate exceeds the mechanical frequency.

arXiv:1611.03842Physical review. B./Physical review. BJul 11, 201732 citations

Nonlinear Microwave Optomechanics

Olga Shevchuk

The nonlinearity is essential for creation of non-classical states of the cavity or mechanical resonator such as squeezed or cat states. A microwave cavity can be made nonlinear by, for instance, adding Josephson junctions. The mechanical resonator is inherently nonlinear. The radiation pressure interaction between cavity and mechanical resonator is also inherently nonlinear but typically under strong drive of the cavity interaction can be linearized. However, if the optomechanical system is in the strong coupling regime nonlinear quantum effects become observable. These three cases provide the motivation for our studies. We start with backaction analysis of the classical regime of a dc SQUID (superconducting quantum interference device) with an embedded mechanical resonator. Then, we perform quantum analysis to understand how the asymmetry of two Josephson junctions influences the coupling strength of optomechanical interactions such as radiation pressure, cross-Kerr and single-photon beam splitter. Using variational method and self-consistent harmonic approximation we estimate the influence of the radiation pressure coupling and Kerr nonlinearity of the cavity on the effective frequency and dissipation of the cavity. The second part of this thesis focuses on the nonlinearity of the mechanical resonator coupled to the optical/microwave cavity. We study in details the nonlinear optomechanical response and draw the response map to summarize all results of the overcoupled and undercoupled cavity for the red and blue sidebands additionally to the weak and strong drive powers. In the end, w e confirm the developed theory by using it to numerically fit the experimental results.The nonlinearity is essential for creation of non-classical states of the cavity or mechanical resonator such as squeezed or cat states. A microwave cavity can be made nonlinear by, for instance, adding Josephson junctions. The mechanical resonator is inherently nonlinear. The radiation pressure interaction between cavity and mechanical resonator is also inherently nonlinear but typically under strong drive of the cavity interaction can be linearized. However, if the optomechanical system is in the strong coupling regime nonlinear quantum effects become observable. These three cases provide the motivation for our studies. We start with backaction analysis of the classical regime of a dc SQUID (superconducting quantum interference device) with an embedded mechanical resonator. Then, we perform quantum analysis to understand how the asymmetry of two Josephson junctions influences the coupling strength of optomechanical interactions such as radiation pressure, cross-Kerr and single-photon beam splitter. Using variational method and self-consistent harmonic approximation we estimate the influence of the radiation pressure coupling and Kerr nonlinearity of the cavity on the effective frequency and dissipation of the cavity. The second part of this thesis focuses on the nonlinearity of the mechanical resonator coupled to the optical/microwave cavity. We study in details the nonlinear optomechanical response and draw the response map to summarize all results of the overcoupled and undercoupled cavity for the red and blue sidebands additionally to the weak and strong drive powers. In the end, w e confirm the developed theory by using it to numerically fit the experimental results.

Jan 1, 20170 citations

Coupling microwave photons to a mechanical resonator using quantum interference

Ines Corveira Rodrigues, Daniel Bothner, Gary Alexander Steele

The field of optomechanics has emerged as leading platform for achieving quantum control of macroscopic mechanical objects. Implementations of microwave optomechanics to date have coupled microwave photons to mechanical resonators using a moving capacitance. While simple and effective, the capacitive scheme suffers from limitations on the maximum achievable coupling strength. Here, we experimentally implement a fundamentally different approach: flux-mediated optomechanical coupling. In this scheme, mechanical displacements modulate the flux in a superconducting quantum interference device (SQUID) that forms the inductor of a microwave resonant circuit. We demonstrate that this flux-mediated coupling can be tuned in situ by the magnetic flux in the SQUID, enabling nanosecond flux tuning of the optomechanical coupling. Furthermore, we observe linear scaling of the single-photon coupling rate with the in-plane magnetic transduction field, a trend with the potential to overcome the limits of capacitive optomechanics, opening the door for a new generation of groundbreaking optomechanical experiments.The field of optomechanics has emerged as leading platform for achieving quantum control of macroscopic mechanical objects. Implementations of microwave optomechanics to date have coupled microwave photons to mechanical resonators using a moving capacitance. While simple and effective, the capacitive scheme suffers from limitations on the maximum achievable coupling strength. Here, we experimentally implement a fundamentally different approach: flux-mediated optomechanical coupling. In this scheme, mechanical displacements modulate the flux in a superconducting quantum interference device (SQUID) that forms the inductor of a microwave resonant circuit. We demonstrate that this flux-mediated coupling can be tuned in situ by the magnetic flux in the SQUID, enabling nanosecond flux tuning of the optomechanical coupling. Furthermore, we observe linear scaling of the single-photon coupling rate with the in-plane magnetic transduction field, a trend with the potential to overcome the limits of capacitive optomechanics, opening the door for a new generation of groundbreaking optomechanical experiments.

arXiv:1907.01418Nature CommunicationsNov 25, 201960 citations

{g}_{0}

between mechanical and microwave resonators. In a certain limit of parameters, such a coupling can also be seen as a qubit-mediated coupling of two resonators. We show that this scheme allows reaching extremely high

{g}_{0}

. Contrary to the recent proposals for exploiting the nonlinearity of a large radiation-pressure coupling, the main nonlinearity in this setup originates from a cross-Kerr type of coupling between the resonators, where the cavity refractive index depends on the phonon number. The presence of this coupling will allow accessing the individual phonon numbers via the measurement of the cavity.

LC

resonator, and a micromechanical resonator. Our scheme is based on an additional higher-order (generalized) nonlinear cross-Kerr type of coupling, linearly dependent on photon number while quadratically dependent on mechanical phonon number, which can be realized via adjusting the gate charge of the Cooper-pair transistor. We show, both analytically and numerically, that the presence of both cross-Kerr and generalized cross-Kerr nonlinearities not only may give rise to the enhancement of one- and two-photon blockades as well as photon-induced tunneling but can also provide more controllability over them. Furthermore, it is shown that in the regime of zero optomechanical coupling, with the aid of generalized cross-Kerr nonlinearity, one can generate multicomponent mechanical superposition states which exhibit robustness against system dissipations. We also study the steady-state entanglement between the microwave and mechanical modes, the results of which signify the role of generalized cross-Kerr nonlinearity in enhancing the entanglement in the regime of large red detuning. The proposed generalized cross-Kerr optomechanical system can find potential applications in microwave quantum sensing, quantum telecommunication, and quantum information protocols.