Periodic Reporting for period 1 - SuperMeQ (Exploring nonclassical states of center-of-mass mechanical motion with superconducting magneto- and levitomechanics)
Okres sprawozdawczy: 2022-10-01 do 2024-03-31
Quantum technologies rely on the creation, manipulation, and read-out of nonclassical states. Any quantum advantage is hampered by the undesired, unavoidable and largely uncontrollable coupling to the environment, resulting in decoherence of quantum states. Counteracting and minimizing decoherence is a major driver of technology development in quantum technologies.
Nonclassical states, however, must be generated first. To do so, a system of interest is coupled to another (quantum) system. If the coupling rate between the systems exceeds all decoherence rates, quantum states can be generated.
Mechanical resonators have been recently added to the quantum technology hardware toolbox. They open novel possibilities in quantum technologies, foremost in quantum sensing, as novel force and inertial sensing platforms, as well as in quantum networks in the form of quantum amplifiers, quantum memories and quantum transducers. In addition, mechanical resonators are a leading system to test the very foundations of quantum physics in the form of massive quantum probes.
SuperMeQ addresses three basic science goals in quantum technologies, targeting to gain new insights into quantum control over the center-of-mass motion of mechanical resonators. The project is working on : (i) Pushing the limits of decoherence mechanisms of massive objects, (ii) Maximizing the vacuum coupling rate of the center-of-mass motion of a mechanical resonator to a quantum system, and (iii) Generating useful nonclassical states such as squeezed states or states with a negative Wigner function, which have direct relevance for quantum-enhanced force and inertial sensing.
Our project follows a unique approach by realizing two complementary experimental platforms that are tailored to our goals and that are mutually beneficial through parallel development: (a) magnetically levitated superconducting microparticles that access a mass regime spanning more than seven orders of magnitude between picogram and sub-milligram masses, and that are expected to exhibit ultra-low mechanical decoherence, and (b) integrated clamped magnetic or superconducting mechanical resonators that are expected to reach strong vacuum coupling rates.
Key in each of these approaches is that we couple both types of mechanical resonator inductively to superconducting quantum circuits, which allow for full quantum control over the center-of-mass degree of freedom of the mechanical resonators. Our project results will lead to a breakthrough in the development and growth of novel quantum sensing technologies and give new insights into foundational aspects of quantum physics.
Nonclassical states, however, must be generated first. To do so, a system of interest is coupled to another (quantum) system. If the coupling rate between the systems exceeds all decoherence rates, quantum states can be generated.
Mechanical resonators have been recently added to the quantum technology hardware toolbox. They open novel possibilities in quantum technologies, foremost in quantum sensing, as novel force and inertial sensing platforms, as well as in quantum networks in the form of quantum amplifiers, quantum memories and quantum transducers. In addition, mechanical resonators are a leading system to test the very foundations of quantum physics in the form of massive quantum probes.
SuperMeQ addresses three basic science goals in quantum technologies, targeting to gain new insights into quantum control over the center-of-mass motion of mechanical resonators. The project is working on : (i) Pushing the limits of decoherence mechanisms of massive objects, (ii) Maximizing the vacuum coupling rate of the center-of-mass motion of a mechanical resonator to a quantum system, and (iii) Generating useful nonclassical states such as squeezed states or states with a negative Wigner function, which have direct relevance for quantum-enhanced force and inertial sensing.
Our project follows a unique approach by realizing two complementary experimental platforms that are tailored to our goals and that are mutually beneficial through parallel development: (a) magnetically levitated superconducting microparticles that access a mass regime spanning more than seven orders of magnitude between picogram and sub-milligram masses, and that are expected to exhibit ultra-low mechanical decoherence, and (b) integrated clamped magnetic or superconducting mechanical resonators that are expected to reach strong vacuum coupling rates.
Key in each of these approaches is that we couple both types of mechanical resonator inductively to superconducting quantum circuits, which allow for full quantum control over the center-of-mass degree of freedom of the mechanical resonators. Our project results will lead to a breakthrough in the development and growth of novel quantum sensing technologies and give new insights into foundational aspects of quantum physics.
In the first period of the SuperMeQ project (months M1 to M18) we focused mainly on developing the underlying experimental platform, understanding decoherence, and engineering coupling strengths.
We made progress in levitating sub-microgram superconducting spheres at millikelvin temperatures. To achieve this, we used two different experimental platforms. One platform relies on a bulky and the other platform on a chip-based magnetic trap. We could verify that the levitated particle can have a large mechanical quality factor of Q>10^7. We identified possible reasons hampering the Q factor in the chip-based platform to 10^5. We demonstrated read out of the center-of-mass (COM) motion of the levitated particle by optical means via imaging on a CCD camera as well as by magnetic means via inductive coupling to a SQUID. Finally, we demonstrated inductive coupling of the COM motion to a flux-tunable resonator, a major achievement of SuperMeQ. Further, we suggested alternative trap geometries relying on guiding magnetic fields via superconducting bodies and analyzed trap conditions for non-spherical objects, which offer additional degrees of freedom for state manipulation.
We demonstrated that the Kerr nonlinearity intrinsic in a superconducting cavity that contains a SQUID loop can be beneficial in cooling the COM motion of a coupled mechanical resonator. These types of superconducting cavities are used by all experimental nodes within SuperMeQ. One can achieve a lower phonon occupation for certain parameter regimes compared to cooling with a linear cavity, which we demonstrated experimentally. We developed the necessary theory and achieved new results in cooling close to and beyond bistability and in understanding some unexpected behaviour when measuring the transmission of a Kerr cavity. We have now theoretical tools at hand to calibrate the phonon occupation of the COM motion of the mechanical resonators we use. This is key in characterizing and understanding the complete system.
Our clamped systems reach now a coupling strength to cavity decay rate ratio of up to 0.025. We have a clear route to increase this ratio even further by at least one order of magnitude to between 0.25 to 0.4.
We put much focus on improving the coherence of superconducting cavities by improving their fabrication process and by analysing novel coupling geometries. We reach single-photon cavity quality factors of over 1 million without an embedded SQUID, and over 10,000 with an embedded SQUID.
In the experiments at OAEW.I OEAW.V and Chalmers we now use passive cryogenic vibration isolation systems, which drastically reduce the undesired influence of external vibrations on the motion of the mechanical resonators.
We made progress in levitating sub-microgram superconducting spheres at millikelvin temperatures. To achieve this, we used two different experimental platforms. One platform relies on a bulky and the other platform on a chip-based magnetic trap. We could verify that the levitated particle can have a large mechanical quality factor of Q>10^7. We identified possible reasons hampering the Q factor in the chip-based platform to 10^5. We demonstrated read out of the center-of-mass (COM) motion of the levitated particle by optical means via imaging on a CCD camera as well as by magnetic means via inductive coupling to a SQUID. Finally, we demonstrated inductive coupling of the COM motion to a flux-tunable resonator, a major achievement of SuperMeQ. Further, we suggested alternative trap geometries relying on guiding magnetic fields via superconducting bodies and analyzed trap conditions for non-spherical objects, which offer additional degrees of freedom for state manipulation.
We demonstrated that the Kerr nonlinearity intrinsic in a superconducting cavity that contains a SQUID loop can be beneficial in cooling the COM motion of a coupled mechanical resonator. These types of superconducting cavities are used by all experimental nodes within SuperMeQ. One can achieve a lower phonon occupation for certain parameter regimes compared to cooling with a linear cavity, which we demonstrated experimentally. We developed the necessary theory and achieved new results in cooling close to and beyond bistability and in understanding some unexpected behaviour when measuring the transmission of a Kerr cavity. We have now theoretical tools at hand to calibrate the phonon occupation of the COM motion of the mechanical resonators we use. This is key in characterizing and understanding the complete system.
Our clamped systems reach now a coupling strength to cavity decay rate ratio of up to 0.025. We have a clear route to increase this ratio even further by at least one order of magnitude to between 0.25 to 0.4.
We put much focus on improving the coherence of superconducting cavities by improving their fabrication process and by analysing novel coupling geometries. We reach single-photon cavity quality factors of over 1 million without an embedded SQUID, and over 10,000 with an embedded SQUID.
In the experiments at OAEW.I OEAW.V and Chalmers we now use passive cryogenic vibration isolation systems, which drastically reduce the undesired influence of external vibrations on the motion of the mechanical resonators.
We achieved the following published results in the 1st period of SuperMeQ (M1-M18) that go beyond the state-of-the-art:
-We realized magnetic levitation of superconducting microparticles at millikelvin temperatures: Phys. Rev. Applied 19, 054047 (2023) and Phys. Rev. Lett. 131, 043603 (2023). These demonstrations establish a novel platform that is promising for macroscopic quantum physics and sensing applications. Further research goes along improving coherence, signal transduction efficiency, and control.
-We demonstrated Kerr enhanced back action cooling of COM mechanical motion: Phys. Rev. Lett. 130, 033601 (2023). This result has impact in all systems that employ flux-tuneable cavities (or cavities that contain a Kerr nonlinearity). Further research targets analyzing cooling in a wider parameter space.
-We demonstrated coupling of levitated COM particle motion to a flux-tuneable resonator: arXiv:2401.08854v1 [quant-ph]. This result impacts the prospect of the platform for quantum state control. Further research is needed towards improving transduction efficiency and coherence.
-We realized magnetic levitation of superconducting microparticles at millikelvin temperatures: Phys. Rev. Applied 19, 054047 (2023) and Phys. Rev. Lett. 131, 043603 (2023). These demonstrations establish a novel platform that is promising for macroscopic quantum physics and sensing applications. Further research goes along improving coherence, signal transduction efficiency, and control.
-We demonstrated Kerr enhanced back action cooling of COM mechanical motion: Phys. Rev. Lett. 130, 033601 (2023). This result has impact in all systems that employ flux-tuneable cavities (or cavities that contain a Kerr nonlinearity). Further research targets analyzing cooling in a wider parameter space.
-We demonstrated coupling of levitated COM particle motion to a flux-tuneable resonator: arXiv:2401.08854v1 [quant-ph]. This result impacts the prospect of the platform for quantum state control. Further research is needed towards improving transduction efficiency and coherence.