In classical physics, clocks are open dissipative systems driven from thermal equilibrium and necessarily subject to thermal noise. We describe a quantum clock driven by entropy reduction through measurement. The mechanism consists of a superconducting transmon qubit coupled to an open co-planar resonator. The cavity and qubit are driven by coherent fields and the cavity output is monitored with homodyne detection. We show that the measurement itself induces coherent oscillations, with fluctuating period, in the conditional moments. The clock signal can be extracted from the observed measurement currents and analysed to determine the noise performance. The model demonstrates a fundamental principle of clocks at zero temperature: good clocks require high rates of energy dissipation and consequently entropy generation.
In classical physics, clocks are open dissipative systems driven from thermal equilibrium and necessarily subject to thermal noise. We describe a quantum clock driven by entropy reduction through measurement. The mechanism consists of a superconducting transmon qubit coupled to an open co-planar resonator. The cavity and qubit are driven by coherent fields and the cavity output is monitored with homodyne detection. We show that the measurement itself induces coherent oscillations, with fluctuating period, in the conditional moments. The clock signal can be extracted from the observed measurement currents and analysed to determine the noise performance. The model demonstrates a fundamental principle of clocks at zero temperature: good clocks require high rates of energy dissipation and consequently entropy generation.
We theoretically and experimentally study the precision of a quantum clock near zero temperature, explicitly accounting for the effect of continuous measurement. The clock is created by a superconducting transmon qubit dispersively coupled to an open coplanar resonator. The cavity and qubit are driven by coherent fields, and the cavity output is monitored with a quantum-noise-limited amplifier. When the continuous measurement is weak, it induces persistent coherent oscillations (with fluctuating periods) in the conditional moments of the qubit's energy probability distribution, which are manifest in the output of the resonator. On the other hand, strong continuous measurement leads to an incoherent cycle of quantum jumps. We theoretically find an equality for the precision of the clock in each regime. Independently from the equalities, we derive a kinetic uncertainty relation for the precision, and find that both equalities satisfy this uncertainty relation. Finally, we experimentally verify that our quantum clock obeys the kinetic uncertainty relation for the precision, thus making an explicit link between the (kinetic) thermodynamic behavior of the clock and its precision, and achieving an experimental test of a kinetic uncertainty relation in the quantum domain.
All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks require large energy dissipation. For periodic clocks, operating on a limit cycle, this is a consequence of phase diffusion. It is also true for non periodic clocks (for example, radio carbon dating) but due to telegraph noise not to phase diffusion. In this case a key role is played by accurate measurements that decrease entropy, thereby raising the free energy of the clock, and requires access to a low entropy reservoir. In the quantum case, for which thermal noise is replaced by quantum noise (spontaneous emission or tunnelling), measurement plays an essential role for both periodic and non periodic clocks. The paper concludes with a discussion of the Tolman relations and Rovelli's thermal time hypothesis in terms of clock thermodynamics.
A driven linear oscillator and a feedback mechanism are two necessary elements of any classical periodic clock. Here, we introduce a fully quantum clock using a driven oscillator in the quantum regime and coherent quantum feedback. We show that if we treat the model semiclassically, this system supports limit cycles, or self-sustained oscillations, as needed for a periodic clock. We then analyze the noise of the system quantum mechanically and prove that the accuracy of this clock is higher compared with the clock implemented with the classical measurement feedback. We experimentally implement the model using two superconducting cavities with incorporated Josephson junctions and microwave circulators for the realization of the quantum feedback. We confirm the appearance of the limit cycle and study the clock accuracy both in frequency and time domains. Under specific conditions of noisy driving, we observe that the clock oscillations are more coherent than the drive, pointing towards the implementation of a quantum autonomous clock.
Abstract We consider a periodic quantum clock based on cooperative resonance fluorescence at zero temperature. The semi-classical dynamics exhibit a Hopf bifurcation to a limit cycle. In the quantum case, this system has an exact steady state and the limit cycle appears in conditional quantum dynamics under homodyne detection. We show that the intrinsic quantum phase diffusion on the limit cycle leads to fluctuations in the period. By simulating the stochastic master equation for homodyne detection, we extract the statistical properties of the clock period. We show that the precision of the clock satisfies the quantum-thermodynamic kinetic uncertainty relations. As energy dissipation increases, the clock’s quality improves, fully validating, in a quantum stochastic system, the link between energy dissipation and clock precision.
Physical devices operating out of equilibrium are affected by thermal fluctuations, limiting their operational precision. This issue is particularly pronounced at microscopic and quantum scales, where its mitigation requires additional entropy dissipation. Understanding this constraint is important for both fundamental physics and technological design. Clocks, for example, need a thermodynamic flux towards equilibrium to measure time, resulting in a minimum entropy dissipation per clock tick. Although classical and quantum models often show a linear relationship between precision and dissipation, the ultimate bounds on this relationship remain unclear. Here we present an autonomous quantum many-body clock model that achieves clock precision that scales exponentially with entropy dissipation. This is enabled by coherent transport in a spin chain with tailored couplings, where dissipation is confined to a single link. The result demonstrates that coherent quantum dynamics can surpass the traditional thermodynamic precision limits, potentially guiding the development of future high-precision, low-dissipation quantum devices.
Why are classical theories often sufficient to describe the physics of our world even though everything around us is entirely composed of microscopic quantum systems? The boundary between these two fundamentally dissimilar theories remains an unsolved problem in modern physics. Position measurements of small objects allow us to probe the area where the classical approximation breaks down. In quantum mechanics, Heisenbergâ s uncertainty principle dictates that any measurement of the position must be accompanied by measurement induced back-action---in this case manifested as an uncertainty in the momentum. In recent years, cavity optomechanics has become a powerful tool to perform precise position measurements and investigate their fundamental limitations. The utilization of optical micro-cavities greatly enhances the interaction between light and state-of-the-art nanomechanical oscillators. Therefore, quantum mechanical phenomena have been successfully observed in systems far beyond the microscopic world. In such a cavity optomechanical system, the fluctuations in the position of the oscillator are transduced onto the phase of the light, while fluctuations in the amplitude of the light disturb the momentum of the oscillator during the measurement. As a consequence, correlations are established between the amplitude and phase quadrature of the probe light. However, so far, observation of quantum effects has been limited exclusively to cryogenic experiments, and access to the quantum regime at room temperature has remained an elusive goal because the overwhelming amount of thermal motion masks the weak quantum effects. This thesis describes the engineering of a high-performance cavity optomechanical device and presents experimental results showing, for the first time, the broadband effects of quantum back-action at room temperature. The device strongly couples mechanical and optical modes of exceptionally high quality factors to provide a measurement sensitivity ∼104 times below the requirement to resolve the zero-point fluctuations of the mechanical oscillator. The quantum back-action is then observed through the correlations created between the probe light and the motion of the nanomechanical oscillator. A so-called â variational measurementâ , which detects the transmitted light in a homodyne detector tuned close to the amplitude quadrature, resolves the quantum noise due to these correlations at the level of 10\% of the thermal noise over more than an octave of Fourier frequencies around mechanical resonance. Moreover, building on this result, an additional experiment demonstrates the ability to achieve quantum enhanced metrology. In this case, the generated quantum correlations are used to cancel quantum noise in the measurement record, which then leads to an improved relative signal-to-noise ratio in measurements of an external force. In conclusion, the successful observation of broadband quantum behavior on a macroscopic object at room temperature is an important milestone in the field of cavity optomechanics. Specifically, this result heralds the rise of optomechanical systems as a platform for quantum physics at room temperature and shows promise for generation of ponderomotive squeezing in room-temperature interferometers.