When a measurement observable does not commute with a quantum system's Hamiltonian, the energy of the measured system is typically not conserved during the measurement. Instead, energy can be transferred between the measured system and the meter. In this work, we experimentally investigate the energetics of noncommuting measurements in a circuit quantum electrodynamics system containing a transmon qubit embedded in a 3D microwave cavity. We show through spectral analysis of the cavity photons that a frequency shift is imparted on the probe, in balance with the associated energy changes of the qubit. Our experiment provides new insights into foundations of quantum measurement, as well as a better understanding of the key mechanisms at play in quantum energetics. Published by the American Physical Society 2024
When a measurement observable does not commute with a quantum system's Hamiltonian, the energy of the measured system is typically not conserved during the measurement. Instead, energy can be transferred between the measured system and the meter. In this work, we experimentally investigate the energetics of noncommuting measurements in a circuit quantum electrodynamics system containing a transmon qubit embedded in a 3D microwave cavity. We show through spectral analysis of the cavity photons that a frequency shift is imparted on the probe, in balance with the associated energy changes of the qubit. Our experiment provides new insights into foundations of quantum measurement, as well as a better understanding of the key mechanisms at play in quantum energetics. Published by the American Physical Society 2024
Quantum measurements are known to affect the state of the measured system. Such a measurement backaction is due to the interaction of the quantum system with the measuring device. When the measured observable and the system's Hamiltonian do not commute, the backaction can lead to a mean energy change of the system. This energy change has been dubbed "quantum heat" and, in association with feedback processes and/or the interaction with thermal bath(s), proves to be a genuinely quantum resource to fuel new kinds quantum engines. We propose such a measurement powered engine exploiting the non-commutativity of local and non-local operations on a bipartite quantum system.We then investigate the origin of the quantum heat. Even if one cannot model the full dynamics of a measurement due to the collapse of the wavefunction, the energetic aspects can still be investigated by modeling the so-called pre-measurement. During this step, the system interacts and gets correlated with a quantum system which can be viewed as a small part of the measuring apparatus and called the quantum meter. Ideally, at the end of this process, the system's reduced state will be fully decohered in the measurement basis, thus corresponding to the averaged collapsed output states given by the measurement postulate. We find that the quantum heat received by the measured system corresponds to the energy necessary to turn off the coupling between the meter and the system. Using generalized definitions of heat and work, we moreover characterize the work and heat nature of these energy exchanges.Tracing the source of this energy one step further, we propose an autonomous description of a measurement. This is done by considering a flying qubit measured by the quantum field of the cavity it crosses. The interaction being position dependent, the kinetic degree of freedom is providing the required energy to switch on and off the interaction between the qubit and the meter field. A full quantum treatment allows us to evaluate the impact of the finite spatial and momentum extension of the qubit wavepacket. Since the kinetic degree of freedom can be affected by the interaction, it does not simply generate a time dependent Hamiltonian for the other degrees of freedom. We find the correction to this ideal dynamic and analyse its consequences on the nature of the energy fluxes. %spread/extension/broadnessTaking the opposite point of view, we compare the measurement cost of a qubit by a field propagating in a waveguide, depending on the initial state of the field. In the context of a circuit quantum electrodynamics setup, we find that thermal and coherent fields induce the same backaction on the qubit given the same energy constraints.The results presented and discussed in this thesis contribute to unravel the mysterious effects and mechanisms due to quantum measurements. Notably, they give an outlook to further analyse quantum measurement-based engines and to understand the energetic resource that measurements cost and constitute at the same time.
Circuit quantum electrodynamics (cQED), exemplified by a coupled system of a superconducting qubit and a microwave cavity, is a powerful framework for the quantum control and measurement of macroscopic quantum states in solid-state circuits. Quantum circuits based on superconducting qubits have emerged as one of the leading platforms in the pursuit of fault-tolerant quantum computing. Despite significant progress in extending qubit lifetimes, refining experimental protocols, and scaling up quantum processors, errors arising from the control and measurement of superconducting qubits continue to hinder the realization of a universal quantum computer. To investigate the error mechanisms for state-of-the-art qubits, we realize long-lived superconducting transmon qubits that exhibit fluctuating lifetimes, with an average of 0.2 ms and a maximum exceeding 0.4 ms. We then investigate their dominant error mechanism. By introducing novel time-resolved error measurements that are synchronized with the operation of the pulse tube cooler in a dilution refrigerator, we find that mechanical vibrations from the pulse tube induce nonequilibrium dynamics in highly coherent qubits, leading to their correlated bit-flip errors. Our findings not only deepen our understanding of qubit error mechanisms but also provide valuable insights into potential error-mitigation strategies for achieving fault tolerance by decoupling superconducting qubits from their mechanical environments. We also present a novel scheme for operating a cQED system in a regime where the cavity is largely displaced. We find that a qubit drive at the bare cavity frequency can effectively displace the cavity field while minimizing the cavity-drive-induced dephasing and the ac Stark shift. Furthermore, we demonstrate that standard cQED protocols, such as qubit control, readout, and cavity single-photon generation, remain compatible with largely displaced cavity fields, even beyond the critical photon number. These findings open new pathways for exploring cQED dynamics in large-photon-number regimes, including the study of nonlinear phenomena in microwave cavities, the saturation of two-level system baths for extending the coherence of microwave quantum states, and the acceleration of the dispersive readout. Finally, mechanical resonators have emerged as integral components in quantum computing for storing and transducing quantum information. Low-frequency mechanical resonators, with extremely low energy dissipation rates, are particularly interesting for extending the lifetimes of stored quantum information. However, integrating low-frequency mechanical resonators with qubits is challenging because their small energy gaps make coherent energy exchange and ground-state preparation difficult. In this thesis, we report the first steps towards the characterization of a hybrid quantum device, consisting of a Transmon qubit and a circuit optomechanical system, both coupled to a 3D microwave cavity.
Thermodynamics constrains changes to the energy of a system, both deliberate and random, via its first and second laws. When the system is not in equilibrium, fluctuation theorems such as the Jarzynski equality further restrict the distributions of deliberate work done. Such fluctuation theorems have been experimentally verified in small, nonequilibrium quantum systems undergoing unitary or decohering dynamics. Yet, their validity in systems governed by a non-Hermitian Hamiltonian has long been contentious due to the false premise of the Hamiltonian's dual and equivalent roles in dynamics and energetics. Here we show that work fluctuations in a non-Hermitian qubit obey the Jarzynski equality even if its Hamiltonian has complex or purely imaginary eigenvalues. With postselection on a dissipative superconducting circuit undergoing a cyclic parameter sweep, we experimentally quantify the work distribution using projective energy measurements and show that the fate of the Jarzynski equality is determined by the parity-time symmetry of, and the energetics that result from, the corresponding non-Hermitian, Floquet Hamiltonian. By distinguishing the energetics from non-Hermitian dynamics, our results provide the recipe for investigating the nonequilibrium quantum thermodynamics of such open systems. Published by the American Physical Society 2024
We investigate the anomalous energy change of the measurement apparatus when a qubit is measured in bases that do not commute with energy. We model two possible measurement implementations: one is a quantum clock model with a completely time-independent Hamiltonian, while the other is a Jaynes-Cummings model that is time-dependent but conserves the total excitation number. We look at the mean energy change of the measurement apparatus in both models, conditioned on the qubit postselection, and we find that this change can be much greater than the level spacing of the qubit, like an anomalous weak value. In the clock model, the expression for the apparatus energy shift explicitly contains the weak value of the qubit Hamiltonian. However, in our case, no explicit weak measurements are carried out. Our two models give different results, which we explain to be a consequence of the nondegenerate spectrum of the Jaynes-Cummings model. We compare our calculations in the Jaynes-Cummings model with the experimental data of J. Stevens et al., [Phys. Rev. Lett. 129, 110601 (2022)], and we find good agreement when the conditions of our derivation are valid.
Measuring an observable which does not commute with the Hamiltonian of a quantum system usually modifies the mean energy of this system. In an autonomous measurement scheme, coupling the system to a quantum meter, the system's energy change must be compensated by the meter's energy change. Here, we theoretically study such an autonomous meter-system dynamics: a qubit interacting dispersively with a light pulse propagating in a one-dimensional waveguide. The phase of the light pulse is shifted, conditioned to the qubit's state along the z direction, while the orientation of the qubit Hamiltonian is arbitrary. As the interaction is dispersive, photon number is conserved so that energy balance has to be attained by spectral deformations of the light pulse. Building on analytical and numerical solutions, we reveal the mechanism underlying this spectral deformation and display how it compensates for the qubit's energy change. We explain the formation of a three-peak structure of the output spectrum and we provide the conditions under which this is observable.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ‘‘meter’’ measuring the other. We have performed a ‘‘quantum nondemolition’’ measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (‘‘Schrodinger cat’’) gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schrodinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.