Measurement Backaction Research Articles

Enhancement of quantum synchronization via continuous measurement and feedback control

We study synchronization of a quantum van der Pol oscillator with a harmonic drive and demonstrate that quantum synchronization can be enhanced by performing continuous homodyne measurement on an additional bath linearly coupled to the oscillator and applying feedback control to the oscillator. The phase coherence of the oscillator is increased by reducing quantum fluctuations via the continuous measurement, whereas the measurement backaction inevitably induces fluctuations around the phase-locking point. We propose a simple feedback policy for suppressing measurement-induced fluctuations by adjusting the frequency of the harmonic drive, which results in enhancement of quantum synchronization. We further demonstrate that the maximum enhancement of quantum synchronization is achieved by performing quantum measurement on the quadrature angle at which the phase diffusion of the oscillator is the largest and the maximal information on the oscillator phase is extracted.

Feedback induced magnetic phases in binary Bose-Einstein condensates.

Weak measurement in tandem with real-time feedback control is a new route toward engineering novel nonequilibrium quantum matter. Here we develop a theoretical toolbox for quantum feedback control of multicomponent Bose-Einstein condensates (BECs) using backaction-limited weak measurements in conjunction with spatially resolved feedback. Feedback in the form of a single-particle potential can introduce effective interactions that enter into the stochastic equation governing system dynamics. The effective interactions are tunable and can be made analogous to Feshbach resonances-spin independent and spin dependent-but without changing atomic scattering parameters. Feedback cooling prevents runaway heating due to measurement backaction and we present an analytical model to explain its effectiveness. We showcase our toolbox by studying a two-component BEC using a stochastic mean-field theory, where feedback induces a phase transition between easy-axis ferromagnet and spin-disordered paramagnet phases. We present the steady-state phase diagram as a function of intrinsic and effective spin-dependent interaction strengths. Our result demonstrates that closed-loop quantum control of Bose-Einstein condensates is a powerful tool for quantum engineering in cold-atom systems.

Entropy production in continuously measured Gaussian quantum systems

The entropy production rate is a key quantity in nonequilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress toward its full grasping. By using a phase space-based approach, here we take the current framework for the assessment of thermodynamic irreversibility all the way to quantum regimes by characterizing entropy production—and its rate—resulting from the continuous monitoring of a Gaussian system. This allows us to formulate a sharpened second law of thermodynamics that accounts for the measurement back action and information gain from a continuously monitored system. We illustrate our framework in a series of physically relevant examples.

Minimizing Backaction through Entangled Measurements.

When an observable is measured on an evolving coherent quantum system twice, the first measurement generally alters the statistics of the second one, which is known as measurement backaction. We introduce, and push to its theoretical and experimental limits, a novel method of backaction evasion, whereby entangled collective measurements are performed on several copies of the system. This method is inspired by a similar idea designed for the problem of measuring quantum work [Perarnau-Llobet etal., Phys. Rev. Lett. 118, 070601 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.070601]. By using entanglement as a resource, we show that the backaction can be extremely suppressed compared to all previous schemes. Importantly, the backaction can be eliminated in highly coherent processes.

Ancilla-assisted probing of temporal quantum correlations of large spins

When measuring quantum spins at two or more different times, the later measurements are affected by measurement backaction occurring due to the earlier measurements. This makes the measurement of temporal quantum correlation functions challenging. In this paper, I propose a measurement protocol that mitigates the effect of measurement backaction by exploiting spin selection rules. I show that, under suitable conditions, the effect of measurement backaction on two-time quantum correlations becomes negligible when probing a system consisting of spins with large spin quantum numbers $l\gg s$ by coupling it to a spin-$s$ ancilla degree of freedom. A potential application of such a measurement protocol is the probing of an array of Bose-Einstein condensates by light.

Backaction-free measurement of quantum correlations via quantum time-domain interferometry

Time-domain interferometry (TDI) is a method to probe space-time correlations among particles in condensed matter systems. Applying TDI to quantum systems raises the general question, whether two-time correlations can be reliably measured without adverse impact of the measurement backaction onto the dynamics of the system. Here, we show that a recently developed quantum version of TDI (QTDI) indeed can access the full quantum-mechanical two-time correlations without backaction. We further generalize QTDI to weak classical continuous-mode coherent input states, alleviating the need for single-photon input fields. Finally, we interpret our results by splitting the space-time correlations into two parts. While the first one is associated to projective measurements and thus insensitive to backaction, we identify the second contribution as arising from the coherence properties of the state of the probed target system, such that it is perturbed or even destroyed by measurements on the system.

Extending qubit coherence by adaptive quantum environment learning

Decoherence, resulting from unwanted interaction between a qubit and its environment, poses a serious challenge towards the development of quantum technologies. Recently, researchers have started analysing how real-time Hamiltonian learning approaches, based on estimating the qubit state faster than the environmental fluctuations, can be used to counteract decoherence. In this work, we investigate how the back-action of the quantum measurements used in the learning process can be harnessed to extend qubit coherence. We propose an adaptive protocol that, by learning the qubit environment, narrows down the distribution of possible environment states. While the outcomes of quantum measurements are random, we show that real-time adaptation of measurement settings (based on previous outcomes) allows a deterministic decrease of the width of the bath distribution, and hence an increase of the qubit coherence. We numerically simulate the performance of the protocol for the electronic spin of a nitrogen-vacancy centre in diamond subject to a dilute bath of 13C nuclear spin, finding a considerable improvement over the performance of non-adaptive strategies.

Quantum Rifling: Protecting a Qubit from Measurement Back Action.

Quantum mechanics postulates that measuring the qubit's wave function results in its collapse, with the recorded discrete outcome designating the particular eigenstate that the qubit collapsed into. We show that this picture breaks down when the qubit is strongly driven during measurement. More specifically, for a fast evolving qubit the measurement returns the time-averaged expectation value of the measurement operator, erasing information about the initial state of the qubit while completely suppressing the measurement backaction. We call this regime quantum rifling, as the fast spinning of the Bloch vector protects it from deflection into either of its eigenstates. We study this phenomenon with two superconducting qubits coupled to the same probe field and demonstrate that quantum rifling allows us to measure either one of the qubits on demand while protecting the state of the other from measurement backaction. Our results allow for the implementation of selective readout multiplexing of several qubits, contributing to the efficient scaling up of quantum processors for future quantum technologies.

Emergence of singularities from decoherence: Quantum catastrophes

We use a master equation to study the dynamics of two coupled macroscopic quantum systems (e.g.\ a Josephson junction made of two Bose-Einstein condensates or two spin states of an ensemble of trapped ions) subject to a weak continuous measurement. If the coupling between the two systems is suddenly switched on the resulting dynamics leads to caustics (fold and cusp catastrophes) in the number-difference probability distribution, and at the same time the measurement gradually induces a quantum-to-classical transition. Decoherence is often invoked to help resolve paradoxes associated with macroscopic quantum mechanics, but here, on the contrary, caustics are well-behaved in the quantum (many-particle) theory and divergent in the classical (mean-field) theory. Caustics thus represent a breakdown of the classical theory towards which decoherence seems to inevitably lead. We find that measurement backaction plays a crucial role in softening the resulting singularities and calculate the modification to the Arnol'd index which governs the scaling of the caustic's amplitude with the number of atoms. The Arnol'd index acts as a critical exponent for the formation of singularities during quantum dynamics and its modification by the open nature of the system is analogous to the modification of the critical exponents of phase transitions occurring in open systems.

Single-Shot Nondestructive Detection of Rydberg-Atom Ensembles by Transmission Measurement of a Microwave Cavity.

We present an experimental realization of single-shot nondestructive detection of ensembles of helium Rydberg atoms. We use the dispersive frequency shift of a superconducting microwave cavity interacting with the ensemble. By probing the transmission of the cavity, we determine the number of Rydberg atoms or the populations of Rydberg quantum states when the ensemble is prepared in a superposition. At the optimal microwave probe power, determined by the critical photon number, we reach single-shot detection of the atom number with 13% relative precision for ensembles of about 500Rydberg atoms with a measurement backaction characterized by approximately 2% population transfer.

Probing the many-body localization phase transition with superconducting circuits

Chains of superconducting circuit devices provide a natural platform for studies of synthetic bosonic quantum matter. Motivated by the recent experimental progress in realizing disordered and interacting chains of superconducting transmon devices, we study the bosonic many-body localization phase transition using the methods of exact diagonalization as well as matrix product state dynamics. We estimate the location of transition separating the ergodic and the many-body localized phases as a function of the disorder strength and the many-body on-site interaction strength. The main difference between the bosonic model realized by superconducting circuits and similar fermionic model is that the effect of the on-site interaction is stronger due to the possibility of multiple excitations occupying the same site. The phase transition is found to be robust upon including longer-range hopping and interaction terms present in the experiments. Furthermore, we calculate experimentally relevant local observables and show that their temporal fluctuations can be used to distinguish between the dynamics of Anderson insulator, many-body localization, and delocalized phases. While we consider unitary dynamics, neglecting the effects of dissipation, decoherence and measurement back action, the timescales on which the dynamics is unitary are sufficient for observation of characteristic dynamics in the many-body localized phase. Moreover, the experimentally available disorder strength and interactions allow for tuning the many-body localization phase transition, thus making the arrays of superconducting circuit devices a promising platform for exploring localization physics and phase transition.

The role of system–meter entanglement in controlling the resolution and decoherence of quantum measurements

Measurement processes can be separated into an entangling interaction between the system and a meter and a subsequent readout of the meter state that does not involve any further interactions with the system. In the interval between these two stages, the system and the meter are in an entangled state that encodes all possible effects of the readout in the form of non-local quantum correlations between the system and the meter. Here, we show that the entanglement generated in the system–meter interaction expresses a fundamental relation between the amount of decoherence and the conditional probabilities that describe the resolution of the measurement. Specifically, the entanglement generated by the measurement interaction correlates both the target observable and the back-action effects on the system with sets of non-commuting physical properties in the meter. The choice of readout in the meter determines the trade-off between irreversible decoherence and measurement information by steering the system into a corresponding set of conditional output states. The Hilbert space algebra of entanglement ensures that the irreversible part of the decoherence is exactly equal to the Hellinger distance describing the resolution achieved in the measurement. We can thus demonstrate that the trade-off between measurement resolution and back-action is a fundamental property of the entanglement generated in measurement interactions.

Spontaneous Symmetry Breaking Induced by Quantum Monitoring.

Spontaneous symmetry breaking (SSB) is responsible for structure formation in scenarios ranging from condensed matter to cosmology. SSB is broadly understood in terms of perturbations to the Hamiltonian governing the dynamics or to the state of the system. We study SSB due to quantum monitoring of a system via continuous quantum measurements. The acquisition of information during the measurement process induces a measurement backaction that seeds SSB. In this setting, by monitoring different observables, an observer can tailor the topology of the vacuum manifold, the pattern of symmetry breaking, and the nature of the resulting domains and topological defects.

Force sensing in hybrid Bose-Einstein-condensate optomechanics based on parametric amplification

In this paper, the scheme of a force sensor is proposed which has been composed of a hybrid optomechanical cavity containing an interacting cigar-shaped Bose-Einstein condensate (BEC) where the \textit{s}-wave scattering frequency of the BEC atoms as well as the spring coefficient of the cavity moving end-mirror (the mechanical oscillator) are parametrically modulated. It is shown that in the red-detuned regime and under the so-called impedance-matching condition, the mechanical response of the system to the input signal is enhanced substantially, which leads to the amplification of the weak input signal while the added noises of measurement (backaction noises) can be suppressed and lowered much below the standard quantum limit (SQL). In this way, such a hybrid system operates as an ultra-sensitive force sensor which can amplify the input signal and simultaneously suppress the added noises by controlling the amplitudes of modulation and the system cooperativities. The advantage of the presented nonlinear hybrid system accompanied with the mechanical and atomic modulations in comparison to the bare optomechanical cavities is the enhancement of signal amplification as well as the extension of amplification bandwidth.

Observation of nonclassical measurement statistics induced by a coherent spin environment

We demonstrate the role of measurement back-action of a coherent spin environment on the dynamics of a spin (qubit) coupled to it, by inducing non-classical (Quantum Random Walk like) statistics on its measurement trajectory. We show how the long-life time of the spin-bath allows it to correlate measurements of the qubit over many repetitions. We have used Nitrogen Vacancy centers in diamond as a model system, and the projective single-shot readout of the electron spin at low temperatures to simulate these effects. We show that the proposed theoretical model, explains the experimentally observed statistics and their application for quantum state engineering of spin ensembles towards desired states.

Interpreting weak value amplification with a toy realist model

Constructing an ontology for quantum theory is challenging, in part due to measurement back-action. The Aharonov-Albert-Vaidman weak measurement formalism provides a method to predict measurement results (weak values) when back-action is negligible. The weak value appears analogous to a classical conditional mean, yet can be complex and unbounded. We study weak values in the context of a recent quantum optical experiment involving two-photon interactions. The results of the experiment are reinterpreted within a realist ‘stochastic optics’ model of light. We show that the conditional means of the intensities in the model correspond to the experimentally observed weak values and study the breakdown of the model outside the experimentally probed regime in the limit where the weak value predicts ‘anomalous’ results.

Conditional past-future correlation induced by non-Markovian dephasing reservoirs

Memory effects can be studied through a conditional past-future correlation, which measures departure with respect to a conditional past-future independence valid in a memoryless Markovian regime. In a quantum regime this property leads to an operational definition of quantum non-Markovianity based on three consecutive system measurement processes and postselection [Budini, Phys. Rev. Lett. 121, 240401 (2018)]. Here, we study the conditional past-future correlation for a qubit system coupled to different dephasing environments. Exact solutions are obtained for a quantum spin bath as well as for classically fluctuating random Hamiltonian models. The developing of memory effects and departures from Born-Markov or white-noise approximations are related to a measurement back action that changes the system dynamics between consecutive measurements. It is shown that this effect may develop even when the former system evolution is given by a time-independent Lindblad equation. This unusual non-Markovian case arises when the characteristic parameters of the dynamics become Lorentzian random distributed variables.

Measurement-induced dynamics and stabilization of spinor-condensate domain walls.

Weakly measuring many-body systems and allowing for feedback in real time can simultaneously create and measure new phenomena in quantum systems. We theoretically study the dynamics of a continuously measured two-component Bose-Einstein condensate (BEC) potentially containing a domain wall and focus on the tradeoff between usable information obtained from measurement and quantum backaction. Each weakly measured system yields a measurement record from which we extract real-time dynamics of the domain wall. We show that quantum backaction due to measurement causes two primary effects: domain-wall diffusion and overall heating. The system dynamics and signal-to-noise ratio depend on the choice of measurement observable. We propose a feedback protocol to dynamically create a stable domain wall in the regime where domain walls are unstable, giving a prototype example of Hamiltonian engineering using measurement and feedback.

Sensing electrons during an adiabatic coherent transport passage

We study the detection of electrons undergoing coherent transfer via adiabatic passage (CTAP) in a triple quantum-dot system with a quantum point-contact sensing the change of the middle dot. In the ideal scenario, the protocol amounts to perfect change transfer between the external dots with vanishing occupation of the central dot at all times, rendering the measurement and its backaction moot. Nevertheless, even with minor corrections to the protocol, a small population builds up in the central dot. We study the measurement backaction by a Bayesian formalism simulation of an instantaneous detection at the time of maximal occupancy of the dot. We show that the interplay between the measurement backaction and the non-adiabatic dynamics induce a change of the success probability of the protocol, which quantitatively agrees with a continuous detection treatment. We introduce a correlated measurement signal to certify the non-occupancy of the central dot for a successful CTAP protocol, which, in the weak measurement limit, confirms a vanishing occupation of the central dot. Our proposed correlated-signal purports that proper experimental method by which to confirm CTAP.

Quantum Optomechanics in a Liquid.

We measure the quantum fluctuations of a single acoustic mode in a volume of superfluid He that is coupled to an optical cavity. Specifically, we monitor the Stokes and anti-Stokes light scattered by a standing acoustic wave that is confined by the cavity mirrors. The intensity of these signals (and their cross-correlation) exhibits the characteristic features of the acoustic wave's zero-point motion and the quantum backaction of the intracavity light. While these features are also observed in the vibrations of solid objects and ultracold atomic gases, their observation in superfluid He opens the possibility of exploiting the remarkable properties of this material to access new regimes of quantum optomechanics.