We study nonlinear interferometry applied to a measurement of atomic spin and demonstrate a sensitivity that cannot be achieved by any linear-optical measurement with the same experimental resources. We use alignment-to-orientation conversion, a nonlinear-optical technique from optical magnetometry, to perform a nondestructive measurement of the spin alignment of a cold ${}^{87}\mathrm{Rb}$ atomic ensemble. We observe state-of-the-art spin sensitivity in a single-pass measurement, in good agreement with covariance-matrix theory. Taking the degree of measurement-induced spin squeezing as a figure of merit, we find that the nonlinear technique’s experimental performance surpasses the theoretical performance of any linear-optical measurement on the same system, including optimization of probe strength and tuning. The results confirm the central prediction of nonlinear metrology, that superior scaling can lead to superior absolute sensitivity.

We present two strategies for performing two-qubit operations on the electron spins of an exchange-coupled pair of donors in silicon, using the ability to set the donor nuclear spins in arbitrary states. The effective magnetic detuning of the two electron qubits is provided by the hyperfine interaction when the two nuclei are prepared in opposite spin states. This can be exploited to switch SWAP operations on and off with modest tuning of the electron exchange interaction. Furthermore, the hyperfine detuning enables high-fidelity conditional rotation gates based on selective resonant excitation. The latter requires no dynamic tuning of the exchange interaction at all and offers a very attractive scheme to implement two-qubit logic gates under realistic experimental conditions.

When a measurement has limited strength, only partial information, regarding the initial state, is extracted, and, correspondingly, there is a probability to reverse its effect on the system and retrieve the original state. Recently, a clear and direct quantitative description of this complementary relationship, in terms of a tradeoff relation, was developed by Y. K. Cheong and S. W. Lee. [Phys. Rev. Lett. 109, 150402 (2012)]. Here, this tradeoff relation is experimentally verified using polarization-encoded single photons from a quantum dot. Measurement operators representing a complete range, from not affecting the system to a projection to a single polarization state, are realized. In addition, for each measurement operator, an optimal reversal operator is also implemented. The upper bound of the tradeoff relation is mapped to experimental parameters representing the measurement strength. Our results complement the theoretical work and provide a hands-on characterization of general quantum measurements.

Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have built a series of architecturally scalable QA processors consisting of networks of manufactured interacting spins (qubits). Here, we use qubit tunneling spectroscopy to measure the energy eigenspectrum of two- and eight-qubit systems within one such processor, demonstrating quantum coherence in these systems. We present experimental evidence that, during a critical portion of QA, the qubits become entangled and entanglement persists even as these systems reach equilibrium with a thermal environment. Our results provide an encouraging sign that QA is a viable technology for large-scale quantum computing.

Undoped-graphene (Gr) sheets at low temperatures are known, via random-phase-approximation (RPA) calculations, to exhibit unusual van der Waals (vdW) forces. Here, we show that graphene is the first known system where effects beyond the RPA within each interacting subsystem make qualitative changes to the vdW force, observable via its local exponent $d\log (F)/d\log (D)$. For large separations $D\gtrsim 10\mathrm{nm}$, where only the ${\pi }_z$ vdW forces remain, we find that the Gr-Gr vdW interaction is substantially reduced from the RPA prediction. Its $D$ dependence is very sensitive to the form of the long-wavelength, in-plane many-body enhancement of the velocity of the massless Dirac fermions and may provide independent confirmation of the latter via direct force measurements. The simple connection that we expose is a strong motivation for further refinement of recent successful direct vdW force measurements.

Quasifree field-driven electron trajectories are a key element of strong-field dynamics. Upon recollision with the parent ion, the energy transferred from the field to the electron may be released as attosecond-duration extreme ultaviolet emission in the process of high-harmonic generation. The conventional sinusoidal driver fields set limitations on the maximum value of this energy transfer and the efficient return of the launched electron trajectories. It has been predicted that these limits can be significantly exceeded by an appropriately ramped-up cycle shape [L. E. Chipperfield et al., Phys. Rev. Lett. 102, 063003 (2009)]. Here, we present an experimental realization of similar cycle-shaped waveforms and demonstrate control of the high-harmonic generation process on the single-atom quantum level via attosecond steering of the electron trajectories. With our improved optical cycles, we boost the field ionization launching the electron trajectories, increase the subsequent field-to-electron energy transfer, and reduce the trajectory duration. We demonstrate, in realistic experimental conditions, 2 orders of magnitude enhancement of the generated extreme ultraviolet flux together with an increased spectral extension. This application, which is only one example of what can be achieved with cycle-shaped high-field light waves, has significant implications for attosecond spectroscopy and molecular self-probing.

A shortcut to adiabaticity is a driving protocol that reproduces in a short time the same final state that would result from an adiabatic, infinitely slow process. A powerful technique to engineer such shortcuts relies on the use of auxiliary counterdiabatic fields. Determining the explicit form of the required fields has generally proven to be complicated. We present explicit counterdiabatic driving protocols for scale-invariant dynamical processes, which describe, for instance, expansion and transport. To this end, we use the formalism of generating functions and unify previous approaches independently developed in classical and quantum studies. The resulting framework is applied to the design of shortcuts to adiabaticity for a large class of classical and quantum, single-particle, nonlinear, and many-body systems.

We study a new class of unconventional critical phenomena that is characterized by singularities only in dynamical quantities and has no thermodynamic signatures. One example of such a transition is the recently proposed many-body localization-delocalization transition, in which transport coefficients vanish at a critical temperature with no singularities in thermodynamic observables. Describing this purely dynamical quantum criticality is technically challenging as understanding the finite-temperature dynamics necessarily requires averaging over a large number of matrix elements between many-body eigenstates. Here, we develop a real-space renormalization group method for excited states that allows us to overcome this challenge in a large class of models. We characterize a specific example: the 1 D disordered transverse-field Ising model with generic interactions. While thermodynamic phase transitions are generally forbidden in this model, using the real-space renormalization group method for excited states we find a finite-temperature dynamical transition between two localized phases. The transition is characterized by nonanalyticities in the low-frequency heat conductivity and in the long-time (dynamic) spin correlation function. The latter is a consequence of an up-down spin symmetry that results in the appearance of an Edwards-Anderson-like order parameter in one of the localized phases.

We describe how randomized benchmarking can be used to reconstruct the unital part of any trace-preserving quantum map, which in turn is sufficient for the full characterization of any unitary evolution or, more generally, any unital trace-preserving evolution. This approach inherits randomized benchmarking’s robustness to preparation, measurement, and gate imperfections, thereby avoiding systematic errors caused by these imperfections. We also extend these techniques to efficiently estimate the average fidelity of a quantum map to unitary maps outside of the Clifford group. The unitaries we consider correspond to large circuits commonly used as building blocks to achieve scalable, universal, and fault-tolerant quantum computation. Hence, we can efficiently verify all such subcomponents of a circuit-based universal quantum computer. In addition, we rigorously bound the time and sampling complexities of randomized benchmarking procedures, proving that the required nonlinear estimation problem can be solved efficiently.

We use frequency-entangled photons, generated via spontaneous parametric down conversion, to measure the broadband spectral response of an array of gold nanoparticles exhibiting Fano-type plasmon resonance. Refractive-index sensing of a liquid is performed by measuring the shift of the array resonance. This method is robust in excessively noisy conditions compared with conventional broadband transmission spectroscopy. Detection of a refractive-index change is demonstrated with a noise level 70 times higher than the signal, which is shown to be inaccessible with the conventional transmission spectroscopy. Use of low-photon fluxes makes this method suitable for measurements of photosensitive biosamples and chemical substances.

The application of postselection to a weak quantum measurement leads to the phenomenon of weak values. Expressed in units of the measurement strength, the displacement of a quantum coherent measuring device is ordinarily bounded by the eigenspectrum of the measured observable. Postselection can enable an interference effect that moves the average displacement far outside this range, bringing practical benefits in certain situations. Employing the Fisher-information metric, we argue that the amplified displacement offers no fundamental metrological advantage, due to the necessarily reduced probability of success. Our understanding of metrological advantage is the possibility of a lower uncertainty in the estimate of an unknown parameter with a large number of trials. We analyze a situation in which the detector is pixelated with a finite resolution and in which the detector is afflicted by random displacements: imperfections that degrade the fundamental limits of parameter estimation. Surprisingly, weak-value amplification is no more robust to them than a technique making no use of the amplification effect brought about by a final, postselected measurement.

Quantum fluctuations become particularly relevant in highly frustrated quantum magnets and can lead to new states of matter. We provide a simple and robust scenario for inducing magnetic vortex crystals in frustrated Mott insulators. By considering a quantum paramagnet that has a gapped spectrum with six-fold degenerate low-energy modes, we study the magnetic-field-induced condensation of these modes. We use a dilute gas approximation to demonstrate that a plethora of multi-$\mathbf{Q}$ condensates are stabilized for different combinations of exchange interactions. This rich quantum phase diagram includes magnetic vortex crystals, which are further stabilized by symmetric exchange anisotropies. Because skyrmion and domain-wall crystals have already been predicted and experimentally observed, this novel vortex phase completes the picture of emergent crystals of topologically nontrivial spin configurations.

We report both subdiffraction-limited quantum metrology and quantum-enhanced spatial resolution for the first time in a biological context. Nanoparticles are tracked with quantum-correlated light as they diffuse through an extended region of a living cell in a quantum-enhanced photonic-force microscope. This allows spatial structure within the cell to be mapped at length scales down to 10 nm. Control experiments in water show a 14% resolution enhancement compared to experiments with coherent light. Our results confirm the long-standing prediction that quantum-correlated light can enhance spatial resolution at the nanoscale and in biology. Combined with state-of-the-art quantum light sources, this technique provides a path towards an order of magnitude improvement in resolution over similar classical imaging techniques.

The locking effect is a phenomenon that is unique to quantum information theory and represents one of the strongest separations between the classical and quantum theories of information. The Fawzi-Hayden-Sen locking protocol harnesses this effect in a cryptographic context, whereby one party can encode $n$ bits into $n$ qubits while using only a constant-size secret key. The encoded message is then secure against any measurement that an eavesdropper could perform in an attempt to recover the message, but the protocol does not necessarily meet the composability requirements needed in quantum key distribution applications. In any case, the locking effect represents an extreme violation of Shannon’s classical theorem, which states that information-theoretic security holds in the classical case if and only if the secret key is the same size as the message. Given this intriguing phenomenon, it is of practical interest to study the effect in the presence of noise, which can occur in the systems of both the legitimate receiver and the eavesdropper. This paper formally defines the locking capacity of a quantum channel as the maximum amount of locked information that can be reliably transmitted to a legitimate receiver by exploiting many independent uses of a quantum channel and an amount of secret key sublinear in the number of channel uses. We provide general operational bounds on the locking capacity in terms of other well-known capacities from quantum Shannon theory. We also study the important case of bosonic channels, finding limitations on these channels’ locking capacity when coherent-state encodings are employed and particular locking protocols for these channels that might be physically implementable.

Optomechanical systems can exhibit self-sustained limit cycles where the quantum state of the mechanical resonator possesses nonclassical characteristics such as a strongly negative Wigner density, as was shown recently in a numerical study by Qian et al. [Phys. Rev. Lett. 109, 253601 (2012)]. Here, we derive a Fokker-Planck equation describing mechanical limit cycles in the quantum regime that correctly reproduces the numerically observed nonclassical features. The derivation starts from the standard optomechanical master equation and is based on techniques borrowed from the laser theory due to Haake and Lewenstein. We compare our analytical model with numerical solutions of the master equation based on Monte Carlo simulations and find very good agreement over a wide and so far unexplored regime of system parameters. As one main conclusion, we predict negative Wigner functions to be observable even for surprisingly classical parameters, i.e., outside the single-photon strong-coupling regime, for strong cavity drive and rather large limit-cycle amplitudes. The approach taken here provides a natural starting point for further studies of quantum effects in optomechanics.

Almost 30 years ago, Durnin discovered that an optical beam with a transverse intensity profile in the form of a Bessel function of the first order is immune to the effects of diffraction. Unlike most laser beams, which spread upon propagation, the transverse distribution of these Bessel beams remains constant. Electrons also obey a wave equation (the Schrödinger equation), and therefore Bessel beams also exist for electron waves. We generate an electron Bessel beam by diffracting electrons from a nanoscale phase hologram. The hologram imposes a conical phase structure on the electron wave-packet spectrum, thus transforming it into a conical superposition of infinite plane waves, that is, a Bessel beam. We verify experimentally that these beams can propagate for 0.6 m without measurable spreading and can also reconstruct their intensity distributions after being partially obstructed by an obstacle. Finally, we show by numerical calculations that the performance of an electron microscope can be increased dramatically through use of these beams.

Inspired by the creation of a fast exchange-only qubit [Medford et al., Phys. Rev. Lett. 111, 050501 (2013)], we develop a theory describing the nonlinear dynamics of two such qubits that are capacitively coupled, when one of them is driven resonantly at a frequency equal to its level splitting. We include conditions of strong driving, where the Rabi frequency is a significant fraction of the level splitting, and we consider situations where the splitting for the second qubit may be the same as or different than the first. We demonstrate that coupling between qubits can be detected by reading the response of the second qubit, even when the coupling between them is only of about 1% of their level splittings, and we calculate entanglement between qubits. Patterns of nonlinear dynamics of coupled qubits and their entanglement are strongly dependent on the geometry of the system, and the specific mechanism of interqubit coupling deeply influences dynamics of both qubits. In particular, we describe the development of irregular dynamics in a two-qubit system, explore approaches for inhibiting it, and demonstrate the existence of an optimal range of coupling strength maintaining stability during the operational time.

The future progress of semi-device-independent quantum information science depends crucially on our ability to bound the strength of the nonlocal correlations achievable with finite-dimensional quantum resources. In this work, we characterize quantum nonlocality under local dimension constraints via a complete hierarchy of semidefinite programming relaxations. In the bipartite case, we find that the first level of the hierarchy returns nontrivial bounds in all cases considered, allowing us to study nonlocality scenarios with four measurement settings on one side and twelve on the other in a normal desktop. In the tripartite case, we apply the hierarchy to derive a Bell-type inequality that can only be violated when each of the three parties has local dimension greater than 2, hence certifying three-dimensional tripartite entanglement in a device-independent way. Finally, we show how the new method can be trivially modified to detect nonseparable measurements in two-qubit scenarios.