In quantum thermodynamics, the standard approach to estimate work fluctuations in unitary processes is based on two projective measurements, one performed at the beginning of the process and one at the end. The first measurement destroys any initial coherence in the energy basis, thus preventing later interference effects. In order to decrease this back-action, a scheme based on collective measurements has been proposed in~[PRL 118, 070601 (2017)]. Here, we report its experimental implementation in an optical system. The experiment consists of a deterministic collective measurement on identically prepared two qubits, encoded in the polarisation and path degree of a single photon. The standard two projective measurement approach is also experimentally realized for comparison. Our results show the potential of collective schemes to decrease the back-action of projective measurements, and capture subtle effects arising from quantum coherence.
We propose schemes that are efficient when each pair of qubits undergoes some imperfect collective decoherence with different baths. In the proposed scheme, each pair of qubits is first encoded in a decoherence-free subspace composed of two qubits. Leakage out of the encoding space generated by the imperfection is reduced by the quantum Zeno effect. Phase errors in the encoded bits generated by the imperfection are reduced by concatenation of the decoherence-free subspace with either a three-qubit quantum error correcting code that corrects only phase errors or a two-qubit quantum error detect…
We demonstrate that reversible dephasing via inhomogeneous broadening can greatly reduce collective quantum state rotation errors, and observe the suppression of rotation errors by more than 21 dB in the context of collective population measurements of the spin states of an ensemble of $2.1 \times 10^5$ laser cooled and trapped $^{87}$Rb atoms. The large reduction in rotation noise enables direct resolution of spin state populations 13(1) dB below the fundamental quantum projection noise limit. Further, the spin state measurement projects the system into an entangled state with 9.5(5) dB of di…
Decoherence in quantum computer memory due to the inevitable coupling to the external environment is examined. We take the assumption that all quantum bits (qubits) interact with the same environment rather than the assumption of separate environments for different qubits. It is found that the qubits are decohered collectively. For some kinds of entangled input states, no decoherence occurs at all in the memory even if the qubits are interacting with the environment. Based on this phenomenon, a scheme is proposed for reducing the collective decoherence. We also discuss possible implications of…
In this paper, we investigate theoretically the back-action evading measurement of the collective mode of an interacting atomic Bose-Einstein condensate (BEC) trapped in an optical cavity which is driven coherently by a pump laser with a modulated amplitude. It is shown that for a specified kind of amplitude modulation of the driving laser, one can measure a generalized quadrature of the collective mode of the BEC indirectly through the output cavity field with a negligible backaction noise in the good-cavity limit. Nevertheless, the on-resonance added noise of measurement is suppressed below …
The standard quantum limit constrains the precision of an oscillator position measurement. It arises from a balance between the imprecision and the quantum back-action of the measurement. However, a measurement of only a single quadrature of the oscillator can evade the back-action and be made with arbitrary precision. Here we demonstrate quantum back-action evading measurements of a collective quadrature of two mechanical oscillators, both coupled to a common microwave cavity. The work allows for quantum state tomography of two mechanical oscillators, and provides a foundation for macroscopic…
Dynamic correlations of quantum observables are challenging to measure due to measurement backaction incurred at early times. Recent work [P. Uhrich et al., Phys. Rev. A, 96:022127 (2017)] has shown that ancilla-based noninvasive measurements are able to reduce this backaction, allowing for dynamic correlations of single-site spin observables to be measured. We generalise this result to correlations of arbitrary spin observables and extend the measurement protocol to simultaneous noninvasive measurements which allow for real and imaginary parts of correlations to be extracted from a single set…
We consider decoherence of quantum registers, which consist of the qubits sited approximately periodically in space. The sites of the qubits are permitted to have a small random variance. We derive the explicit conditions under which the qubits can be assumed decohering independently. In other circumstances, the qubits are decohered cooperatively. We describe two kinds of collective decoherence. In each case, a scheme is proposed for reducing the collective decoherence. The schemes operate by encoding the input states of the qubits into some ''subdecoherent'' states.
We consider use of collective variables for description of composite fields as collective phenomena due to the strong coupling regime. We discuss two approaches, where identification of collective variables of complex quantum system does not depend on knowledge of other degrees of freedom: (a) collective variables as parameters of group transformations changing the path integral of the system, and (b) collective variables as background fields for quantum system. In the case (a) we briefly present an approach. In the case (b) we consider fermions in an external scalar field, which serves as a c…
We calculate the energy levels of a system of neutrinos undergoing collective oscillations as functions of an effective coupling strength and radial distance from the neutrino source using the quantum Lanczos (QLanczos) algorithm implemented on IBM Q quantum computer hardware. Our calculations are based on the many-body neutrino interaction Hamiltonian introduced in Ref.\ \cite{Patwardhan2019}. We show that the system Hamiltonian can be separated into smaller blocks, which can be represented using fewer qubits than those needed to represent the entire system as one unit, thus reducing the nois…
We study the collective radiative decay of a system of two two-level emitters coupled to a one-dimensional waveguide in a regime where their separation is comparable to the coherence length of a spontaneously emitted photon. The electromagnetic field propagating in the cavity-like geometry formed by the emitters exerts a retarded backaction on the system leading to strongly non-Markovian dynamics. The collective spontaneous emission rate of the emitters exhibits an enhancement or inhibition beyond the usual Dicke super- and sub-radiance due to a self-consistent coherent time-delayed feedback.
A near perfect, storage time-extended photon echo-based quantum memory protocol has been analyzed by solving the Maxwell-Bloch equations for a backward scheme in a three-level system. The backward photon echo scheme is combined with a controlled coherence conversion process via control Rabi flopping to a third state, where the control Rabi flopping collectively shifts the phase of the ensemble coherence. The propagation direction of photon echoes is coherently determined by the phase matching condition between the data (quantum) and the control (classical) pulses. Herein we discuss the classic…
We experimentally demonstrate optical dipole trapping of a cloud of cold atoms by means of a dynamically coupled mode of a high-finesse cavity. We show that the trap requires a collective action of the atoms, i.e. a single atom would not be trapped under the same laser drive conditions. The atoms pull the frequency of the mode closer to resonance, thereby allowing the necessary light intensity for trapping into the cavity. The back-action of the atoms on the trapping light mode is also manifested by the non-exponential collapse of the trap.
We directly measure the quantized collective motion of a gas of thousands of ultracold atoms, coupled to light in a high-finesse optical cavity. We detect strong asymmetries, as high as 3:1, in the intensity of light scattered into low- and high-energy motional sidebands. Owing to high cavity-atom cooperativity, the optical output of the cavity contains a spectroscopic record of the energy exchanged between light and motion, directly quantifying the heat deposited by a quantum position measurement's backaction. Such backaction selectively causes the phonon occupation of the observed collective…
Spatial correlation functions provide a glimpse into the quantum correlations within a quantum system. Ions in a linear trap collectively form a nonuniform, discretized background on which a scalar field of phonons propagates. Trapped ions have the experimental advantage of each having their own "built-in" motional detector: electronic states that can be coupled, via an external laser, to the ion's vibrational motion. The post-interaction electronic state can be read out with high efficiency, giving a stochastic measurement record whose classical correlations reflect the quantum correlations o…
Current research on micro-mechanical resonators strives for quantum-limited detection of the motion of macroscopic objects. Prerequisite to this goal is the observation of measurement backaction consistent with quantum metrology limits. However, thermal noise presently dominates measurements and precludes ground-state preparation of the resonator. Here we establish the collective motion of an ultracold atomic gas confined tightly within a Fabry-Perot optical cavity as a system for investigating the quantum mechanics of macroscopic bodies. The cavity-mode structure selects a single collective v…
We develop a Gaussian state treatment that allows a transparent quantum description of the continuous, nondestructive imaging of and feedback on a Bose-Einstein condensate. We have previously demonstrated [Phys. Rev. Lett. \textbf{115}, 060401 (2015)] that the measurement back action of stroboscopic imaging leads to selective squeezing and entanglement of quantized density oscillations. Here, we investigate how the squeezing and entanglement are affected by the finite spatial resolution and geometry of the probe laser beam and of the detector and how they can be optimized.
We use a quantum nondemolition measurement to probe the collective pseudospin of an atomic ensemble in a high-finesse optical cavity. We analyze the backaction antisqueezing produced by the measurement process to show that our protocol could create conditional spin squeezing in the atomic ensemble.
Collective measurements can project a system into an entangled state with enhanced sensitivity for measuring a quantum phase, but measurement back-action has limited previous efforts to only modest improvements. Here we use a collective measurement to produce and directly observe, with no background subtraction, an entangled, spin-squeezed state with phase resolution improved in variance by a factor of 10.5(1.5), or 10.2(6) dB, compared to the initially unentangled ensemble of N = 4.8 x 10^5 87Rb atoms. The measurement uses a cavity-enhanced probe of an optical cycling transition to mitigate b…
Creating squeezed and non-classical collective motional many-body states through stroboscopic Rydberg dressing
Institut für Theoretische Physik and Center for Integrated Quantum Science and Technology, Universität Tübingen（蒂宾根大学理论物理研究所与集成量子科学技术中心）；Institute for Applied Physics, University of Bonn（波恩大学应用物理研究所）；RIKEN Center for Quantum Computing (RQC)（理化学研究院量子计算中心）；Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Tübingen（蒂宾根大学物理研究所与集成量子科学技术中心）；School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham（诺丁汉大学物理与天文学学院及量子非平衡系统数学与理论物理中心）
Two-dimensional regular arrays of atoms are a promising platform for quantum networks, with collective subradiant states providing long-lived storage and collimated emission allowing for natural coherent links between arrays in free space. However, a single-layer lattice can only efficiently absorb or emit light symmetrically in the forward and backward directions. Here we show how a bilayer lattice can absorb a single photon either incident from a single direction or an arbitrary superposition of forward and backward propagating components. The excitation can be stored in a subradiant state, …
We generalize a recently developed scheme for monitoring coherent quantum dynamics with good time-resolution and low backaction [Reuther et al., Phys. Rev. Lett. 102, 033602 (2009)] to the case of more complex quantum dynamics of one or several qubits. The underlying idea is to measure with lock-in techniques the response of the quantum system to a high-frequency ac field. We demonstrate that this scheme also allows one to observe quantum dynamics with many frequency scales, such as that of a qubit undergoing Landau-Zener transitions. Moreover, we propose how to measure the entanglement betwee…
As one of the central topics in quantum optics, collective spontaneous emission such as superradiance has been realized in a variety of systems. This work proposes an innovative scheme to coherently control collective emission rates via a self-interference mechanism in a nonlinear waveguide setting. The self-interference is made possible by photon backward scattering incurred by quantum scatterers in a waveguide working as quantum switches. Whether the interference is constructive or destructive is found to depend strongly on the distance between the scatterers and the emitters. The interferen…
We study theoretically a three-mode optomechanical system where two mechanical oscillators are coupled to a single cavity mode. By using two-tone (i.e. amplitude-modulated) driving of the cavity, it is possible to couple the cavity to a single collective quadrature of the mechanical oscillators. In such a way, a back-action-evading measurement of the collective mechanical quadrature is possible. We discuss how this can allow one to measure both quadratures of a mechanical force beyond the full quantum limit, paying close attention to the role of dissipation and experimental imperfections. We a…
