Ioannis Petrides, Jonathan B. Curtis, Marie Wesson, Amir Yacoby, Prineha Narang
Reciprocal and nonreciprocal effects in dielectric and magnetic materials provide crucial information about the microscopic properties of electrons. However, experimentally distinguishing the two has proven to be challenging, especially when the associated effects are extremely small. To this end, we propose a contact-less detection using a cross-cavity device where a material of interest is placed at its centre. We show that the optical properties of the material, such as Kerr and Faraday rotation, or, birefringence, manifest in the coupling between the cavities' electromagnetic modes and in the shift of their resonant frequencies. By calculating the dynamics of a geometrical photonic state, we formulate a measurement protocol based on the quantum metric and quantum process tomography that isolates the individual components of the material's complex refractive index and minimizes the quantum mechanical Cramér-Rao bound on the variance of the associated parameter estimation. Our approach is expected to be applicable across a broad spectrum of experimental platforms including Fock states in optical cavities, or, coherent states in microwave and THz resonators.
Jonathan B. Curtis, Marios H. Michael, Eugene Demler
Control of quantum matter through resonant electromagnetic cavities is a promising route towards establishing control over material phases and functionalities. Quantum paraelectric insulators -- materials which are nearly ferroelectric -- are particularly promising candidate systems for this purpose since they have strongly fluctuating collective modes which directly couple to the electric field. In this work we explore this possibility in a system comprised of a quantum paraelectric sandwiched between two high-quality metal mirrors, realizing a Fabry-Perot type cavity. By developing a full multimode, continuum description we are able to study the effect of the cavity in a spatially resolved way for a variety of system sizes and temperatures. Surprisingly, we find that once a continuum of transverse modes are included the cavity ends up suppressing ferroelectric correlations. This effect arises from the screening out of transverse photons at the cavity boundaries and as a result is confined to the surface of the paraelectric sample. We also explore the temperature dependence of this effect and find it vanishes at high temperatures, indicating it is a purely quantum mechanical effect. We connect our result to calculations of Casimir and Van der Waals forces, which we argue are closely related to the dipolar fluctuations in the quantum paraelectric. Our results are based on a general formalism and are expected to be widely applicable, paving the way towards studies of the quantum electrodynamics of heterostructures featuring multiple materials and phases.
Julian Klein, Zhigang Song, Benjamin Pingault, Florian Dirnberger, Hang Chi, Jonathan B. Curtis, Rami Dana, Rezlind Bushati, Jiamin Quan, Lukas Dekanovsky, Zdenek Sofer, Andrea Alù, Vinod M. Menon, Jagadeesh S. Moodera, Marko Lončar, Prineha Narang, Frances M. Ross
Atomic-level defects in van der Waals (vdW) materials are essential building blocks for quantum technologies and quantum sensing applications. The layered magnetic semiconductor CrSBr is an outstanding candidate for exploring optically active defects owing to a direct gap in addition to a rich magnetic phase diagram including a recently hypothesized defect-induced magnetic order at low temperature. Here, we show optically active defects in CrSBr that are probes of the local magnetic environment. We observe spectrally narrow (1 meV) defect emission in CrSBr that is correlated with both the bulk magnetic order and an additional low temperature defect-induced magnetic order. We elucidate the origin of this magnetic order in the context of local and non-local exchange coupling effects. Our work establishes vdW magnets like CrSBr as an exceptional platform to optically study defects that are correlated with the magnetic lattice. We anticipate that controlled defect creation allows for tailor-made complex magnetic textures and phases with the unique ingredient of direct optical access.
Nicholas R. Poniatowski, Jonathan B. Curtis, Amir Yacoby, Prineha Narang
The collective mode spectrum of a symmetry-breaking state, such as a superconductor, provides crucial insight into the nature of the order parameter. In this context, we present a microscopic weak-coupling theory for the collective modes of a generic multi-component time-reversal symmetry breaking superconductor, and show that fluctuations in the relative amplitude and phase of the two order parameter components are well-defined underdamped collective modes, even in the presence of nodal quasiparticles. We then demonstrate that these "generalized clapping modes" can be detected using a number of experimental techniques including ac electronic compressibility measurements, electron energy loss spectroscopy, microwave spectroscopy, and ultrafast THz spectroscopy. Finally, we discuss the implications of our work as a new form of "collective mode spectroscopy" that drastically expands the number of experimental probes capable of detecting time-reversal symmetry breaking in unconventional superconductors such as Sr$_{\text{2}}$RuO$_{\text{4}}$, UTe$_{\text{2}}$, and moiré heterostructures.
Jonathan B. Curtis, Igor Boettcher, Jeremy T. Young, Mohammad F. Maghrebi, Howard Carmichael, Alexey V. Gorshkov, Michael Foss-Feig
Jun 10, 2020·quant-ph·PDF Photon blockade is the result of the interplay between the quantized nature of light and strong optical nonlinearities, whereby strong photon-photon repulsion prevents a quantum optical system from absorbing multiple photons. We theoretically study a single atom coupled to the light field, described by the resonantly driven Jaynes--Cummings model, in which case the photon blockade breaks down in a second order phase transition at a critical drive strength. We show that this transition is associated to the spontaneous breaking of an anti-unitary PT-symmetry. Within a semiclassical approximation we calculate the expectation values of observables in the steady state. We then move beyond the semiclassical approximation and approach the critical point from the disordered (blockaded) phase by reducing the Lindblad quantum master equation to a classical rate equation that we solve. The width of the steady-state distribution in Fock space is found to diverge as we approach the critical point with a simple power-law, allowing us to calculate the critical scaling of steady state observables without invoking mean-field theory. We propose a simple physical toy model for biased diffusion in the space of occupation numbers, which captures the universal properties of the steady state. We list several experimental platforms where this phenomenon may be observed.
Jonathan B. Curtis, Nikola Maksimovic, Nicholas R. Poniatowski, Amir Yacoby, Bertrand Halperin, Prineha Narang, Eugene Demler
The melting of quasi-long-range superconductivity in two spatial dimensions occurs through the proliferation and unbinding of vortex-antivortex pairs -- a phenomenon known as the Berezinskii-Kosterlitz-Thouless (BKT) transition. Although signatures of this transition have been observed in bulk measurements, these experiments are often complicated, ambiguous, and unable to resolve the rich physics of the vortex unbinding transition. Here we show that local noise magnetometry is a sensitive, noninvasive probe that can provide direct information about the scale-dependent vortex dynamics. In particular, by resolving the distance and temperature dependence of the magnetic noise, it may be possible to experimentally study the renormalization group flow equations of the vortex gas and track the onset of vortex unbinding in situ. Specifically, we predict i) a nonmonotonic dependence of the noise on temperature and ii) the local noise is almost independent of the sample-probe distance at the BKT transition. We also show that noise magnetometry can distinguish Gaussian superconducting order-parameter fluctuations from topological vortex fluctuations and can detect the emergence of unbound vortices. The weak distance dependence at the BKT transition can also be used to distinguish it from quasiparticle background noise. Our predictions may be within experimental reach for a number of unconventional superconductors.
Jonathan B. Curtis, Gil Refael, Victor Galitski
We consider a model of an acoustic black hole formed by a quasi-one dimensional Bose-Einstein condensate with a step-like horizon. This system is analyzed by solving the corresponding Bogoliubov-de Gennes equation with an appropriate matching condition at the jump. When the step is between a subsonic and supersonic flow, a sonic horizon develops and in addition to the scattering coefficients we compute the distribution of the accompanying analogue Hawking radiation. Additionally, in response to the abrupt variation in flow and non-linear Bogoliubov dispersion relation, evanescent solutions of the Bogoliubov-de Gennes equation also appear and decay out from the horizon. We bound this decay length and show that these modes produce a modulation of observables outside the event horizon by their interference with outgoing Hawking flux. We go further and find specific superpositions of ingoing eigenmodes which exhibit coherent cancellation of the Hawking flux outside the horizon but nevertheless have evanescent support outside the black hole. We conclude by speculating that when quasiparticle interactions are included, evanescent modes may yield a leakage of information across the event horizon via interactions between the real outgoing Hawking flux and the virtual evanescent modes, and that we may expect this as a generic feature of models which break Lorentz invariance at the UV (Planck) scale.
Jonathan B. Curtis, Amir Yacoby, Eugene Demler
Atomic scale qubits, as may be realized in nitrogen vacancy (NV) centers in diamond, offer the opportunity to study magnetic field noise with nanometer scale spatial resolution. Using these spin qubits, one can learn a great deal about the magnetic-field noise correlations, and correspondingly the collective-mode spectra, in quantum materials and devices. However, to date these tools have been essentially restricted to studying Gaussian noise processes -- equivalent to linear-response. In this work we will show how to extend these techniques beyond the Gaussian regime and show how to unambiguously measure higher-order magnetic noise cumulants in a local, spatially resolved way. We unveil two protocols for doing this; the first uses a single spin-qubit and different dynamical decoupling sequences to extract non-Markovian and non-Gaussian spin-echo noise. The second protocol uses two-qubit coincidence measurements to study spatially non-local cumulants in the magnetic noise. We then demonstrate the utility of these protocols by considering a model of a bath of non-interacting two-level systems, as well as a model involving spatially correlated magnetic fluctuations near a second-order Ising phase transition. In both cases, we highlight how this technique can be used to measure in a real many-body system how fluctuation dynamics converge towards the central limit theorem as a function of effective bath size. We then conclude by discussing some promising applications and extensions of this method.
Jun-Yi Shan, Jonathan B. Curtis, Mingyao Guo, Chang Jae Roh, C. R. Rotundu, Young S. Lee, Prineha Narang, Tae Won Noh, Eugene Demler, D. Hsieh
Uncovering pathways to optically drive magnetic order-disorder transitions on ultrashort timescales can lead to the realization of novel out-of-equilibrium quantum phenomena. A long-sought pathway is to directly excite a highly non-thermal energy-momentum distribution of magnons, bypassing both charge and lattice degrees of freedom. However, this remains elusive owing to the weak coupling and large momentum mismatch between photons and magnons. Here we demonstrate strong parametric excitation of magnons across the entire Brillouin zone of the antiferromagnetic insulator Sr$_2$Cu$_3$O$_4$Cl$_2$ by periodically modulating the superexchange interaction with the electric field of light. The excitation efficiency is greatly enhanced by tuning to the van Hove singularity in the magnon spectrum, sufficient to transiently collapse the antiferromagnetic state using a pulsed laser field of 10$^9$ V/m. The order parameter recovery timescale increases by over 1000 times as a function of excitation density, reflecting a crossover from high- to low-energy magnon dominated decay dynamics. This electric-field induced parametric magnon pumping mechanism is applicable to a broad range of magnetic insulators and opens up the possibility of dynamically engineering magnon distributions by design.
Jonathan B. Curtis, Nicholas R. Poniatowski, Yonglong Xie, Amir Yacoby, Eugene Demler, Prineha Narang
A recent experiment showed that proximity induced Ising spin-orbit coupling enhances the spin-triplet superconductivity in Bernal bilayer graphene. Here, we show that, due to the nearly perfect spin rotation symmetry of graphene, the fluctuations of the spin orientation of the triplet order parameter suppress the superconducting transition to nearly zero temperature. Our analysis shows that both Ising spin-orbit coupling and in-plane magnetic field can eliminate these low-lying fluctuations and can greatly enhance the transition temperature, consistent with the recent experiment. Our model also suggests the possible existence of a phase at small anisotropy and magnetic field which exhibits quasi-long-range ordered spin-singlet charge 4e superconductivity, even while the triplet 2e superconducting order only exhibits short-ranged correlations. Finally, we discuss relevant experimental signatures.
Nicholas R. Poniatowski, Jonathan B. Curtis, Charlotte G. L. Bøttcher, Victor M. Galitski, Amir Yacoby, Prineha Narang, Eugene Demler
We study the electrodynamics of spin triplet superconductors including dipolar interactions, which give rise to an interplay between the collective spin dynamics of the condensate and orbital Meissner screening currents. Within this theory, we identify a class of spin waves that originate from the coupled dynamics of the spin-symmetry breaking triplet order parameter and the electromagnetic field. In particular, we study magnetostatic spin wave modes that are localized to the sample surface. We show that these surface modes can be excited and detected using experimental techniques such as microwave spin wave resonance spectroscopy or nitrogen-vacancy magnetometry, and propose that the detection of these modes offers a means for the identification of spin triplet superconductivity.
Jonathan B. Curtis, Ankit Disa, Michael Fechner, Andrea Cavalleri, Prineha Narang
By using intense coherent electromagnetic radiation, it may be possible to manipulate the properties of quantum materials very quickly, or even induce new and potentially useful phases that are absent in equilibrium. For instance, ultrafast control of magnetic dynamics is crucial for a number of proposed spintronic devices and can also shed light on the possible dynamics of correlated phases out of equilibrium. Inspired by recent experiments on spin-orbital ferromagnet YTiO$_3$ we consider the nonequilibrium dynamics of Heisenberg ferromagnetic insulator with low-lying orbital excitations. We model the dynamics of the magnon excitations in this system following an optical pulse which resonantly excites infrared-active phonon modes. As the phonons ring down they can dynamically couple the orbitals with the low-lying magnons, leading to a dramatically modified effective bath for the magnons. We show this transient coupling can lead to a dynamical acceleration of the magnetization dynamics, which is otherwise bottlenecked by small anisotropy. Exploring the parameter space more we find that the magnon dynamics can also even completely reverse, leading to a negative relaxation rate when the pump is blue-detuned with respect to the orbital bath resonance. We therefore show that by using specially targeted optical pulses, one can exert a much greater degree of control over the magnetization dynamics, allowing one to optically steer magnetic order in this system. We conclude by discussing interesting parallels between the magnetization dynamics we find here and recent experiments on photo-induced superconductivity, where it is similarly observed that depending on the initial pump frequency, an apparent metastable superconducting phase emerges.
Jonathan B. Curtis, Andrey Grankin, Nicholas R. Poniatowski, Victor M. Galitski, Prineha Narang, Eugene Demler
Cavity control of quantum matter may offer new ways to study and manipulate many-body systems. A particularly appealing idea is to use cavities to enhance superconductivity, especially in unconventional or high-$T_c$ systems. Motivated by this, we propose a scheme for coupling Terahertz resonators to the antiferromagnetic fluctuations in a cuprate parent compound, which are believed to provide the glue for Cooper pairs in the superconducting phase. First, we derive the interaction between magnon excitations of the Neél-order and polar phonons associated with the planar oxygens. This mode also couples to the cavity electric field, and in the presence of spin-orbit interactions mediates a linear coupling between the cavity and magnons, forming hybridized magnon-polaritons. This hybridization vanishes linearly with photon momentum, implying the need for near-field optical methods, which we analyze within a simple model. We then derive a higher-order coupling between the cavity and magnons which is only present in bilayer systems, but does not rely on spin-orbit coupling. This interaction is found to be large, but only couples to the bimagnon operator. As a result we find a strong, but heavily damped, bimagnon-cavity interaction which produces highly asymmetric cavity line-shapes in the strong-coupling regime. To conclude, we outline several interesting extensions of our theory, including applications to carrier-doped cuprates and other strongly-correlated systems with Terahertz-scale magnetic excitations.
Pavel E. Dolgirev, Alfred Zong, Marios H. Michael, Jonathan B. Curtis, Daniel Podolsky, Andrea Cavalleri, Eugene Demler
A number of experiments have evidenced signatures of enhanced superconducting correlations after photoexcitation. Initially, these experiments were interpreted as resulting from quasi-static changes in the Hamiltonian parameters, for example, due to lattice deformations or melting of competing phases. Yet, several recent observations indicate that these conjectures are either incorrect or do not capture all the observed phenomena, which include reflectivity exceeding unity, large shifts of Josephson plasmon edges, and appearance of new peaks in terahertz reflectivity. These observations can be explained from the perspective of a Floquet theory involving a periodic drive of system parameters, but the origin of the underlying oscillations remains unclear. In this paper, we demonstrate that following incoherent photoexcitation, long-lived oscillations are generally expected in superconductors with low-energy Josephson plasmons, such as in cuprates or fullerene superconductor K$_3$C$_{60}$. These oscillations arise from the parametric generation of plasmon pairs due to pump-induced perturbation of the superconducting order parameter. We show that this bi-plasmon response can persist even above the transition temperature as long as strong superconducting fluctuations are present. Our analysis offers a robust framework to understand light-induced superconducting behavior, and the predicted bi-plasmon oscillations can be directly detected using available experimental techniques.
Justin H. Wilson, Jonathan B. Curtis, Victor M. Galitski
It is well established that linear dispersive modes in a flowing quantum fluid behave as though they are coupled to an Einstein-Hilbert metric and exhibit a host of phenomena coming from quantum field theory in curved space, including Hawking radiation. We extend this analogy to any nonrelativistic Goldstone mode in a flowing spinor Bose-Einstein condensate. In addition to showing the linear dispersive result for all such modes, we show that the quadratically dispersive modes couple to a special nonrelativistic spacetime called a Newton-Cartan geometry. The kind of spacetime (Einstein-Hilbert or Newton-Cartan) is intimately linked to the mean-field phase of the condensate. To illustrate the general result, we further provide the specific theory in the context of a pseudo-spin-1/2 condensate where we can tune between relativistic and nonrelativistic geometries. We uncover the fate of Hawking radiation upon such a transition: it vanishes and remains absent in the Newton-Cartan geometry despite the fact that any fluid flow creates a horizon for certain wave numbers. Finally, we use the coupling to different spacetimes to compute and relate various energy and momentum currents in these analog systems. While this result is general, present day experiments can realize these different spacetimes including the magnon modes for spin-1 condensates such as $^{87}$Rb, $^{7}$Li, $^{41}$K (Newton-Cartan), and $^{23}$Na (Einstein-Hilbert).
Jonathan B. Curtis, Nicholas R. Poniatowski, Amir Yacoby, Prineha Narang
Unconventional superconductors have been long sought for their potential applications in quantum technologies and devices. A key challenge impeding this effort is the difficulty associated with probing and characterizing candidate materials and establishing their order parameter. In this Letter, we present a platform that allows us to spectroscopically probe unconventional superconductivity in thin-layer materials via the proximity effect. We show that inducing an s-wave gap in a sample with an intrinsic d-wave instability leads to the formation of bound-states of quasiparticle pairs, which manifest as a collective mode in the d-wave channel. This finding provides a way to study the underlying pairing interactions vicariously through the collective mode spectrum of the system. Upon further cooling of the system we observe that this mode softens considerably and may even condense, signaling the onset of time-reversal symmetry breaking superconductivity. Therefore, our proposal also allows for the creation and study of these elusive unconventional states.
Jonathan B. Curtis, Zachary M. Raines, Andrew A. Allocca, Mohammad Hafezi, Victor M. Galitski
Driving a conventional superconductor with an appropriately tuned classical electromagnetic field can lead to an enhancement of superconductivity via a redistribution of the quasiparticles into a more favorable non-equilibrium distribution -- a phenomenon known as the Eliashberg effect. Here we theoretically consider coupling a two-dimensional superconducting film to the quantized electromagnetic modes of a microwave resonator cavity. As in the classical Eliashberg case, we use a kinetic equation to study the effect of the fluctuating, dynamical electromagnetic field on the Bogoliubov quasiparticles. We find that when the photon and quasiparticle systems are out of thermal equilibrium, a redistribution of quasiparticles into a more favorable non-equilibrium steady-state occurs, thereby enhancing superconductivity in the sample. We predict that by tailoring the cavity environment (e.g. the photon occupation and spectral functions), enhancement can be observed in a variety of parameter regimes, offering a large degree of tunability.
Andrew A. Allocca, Zachary M. Raines, Jonathan B. Curtis, Victor M. Galitski
Following the recent success of realizing exciton-polariton condensates in cavities, we examine the hybridization of cavity photons with the closest analog of excitons within a superconductor, states called Bardasis-Schrieffer (BS) modes. Though BS modes do not typically couple directly to light, one can engineer a coupling with an externally imposed supercurrent, leading to the formation of hybridized Bardasis-Schrieffer-polariton states, which we obtain both via direct solution and through the derivation of an effective Hamiltonian picture for the model. These new excitations have nontrivial overlap with both the original photon states and $d$-wave superconducting fluctuations, implying that their condensation could produce a finite $d$-wave component of the superconducting order parameter--an $s\pm id$ superconducting state.
Pavel E. Dolgirev, Marios H. Michael, Jonathan B. Curtis, Daniele Nicoletti, Michele Buzzi, Michael Fechner, Andrea Cavalleri, Eugene Demler
Recent experiments in the doped cuprates La$_{2-x}$Ba$_x$CuO$_4$ have revealed the emission of anomalous terahertz radiation after impulsive optical excitation. Here, we theoretically investigate the nonlinear electrodynamics of such striped superconductors and explore the origin of the observed radiation. We argue that photoexcitation is converted into a photocurrent by a second-order optical nonlinearity, which is activated by the breaking of inversion symmetry in certain stripe configurations. We point out the importance of including Umklapp photocurrents modulated at the stripe periodicity itself, which impulsively drive surface Josephson plasmons and lead to a resonant structure of outgoing radiation, consistent with the experiments. We speculate on the utility of the proposed mechanism in the context of generating tunable terahertz radiation.
Jonathan B. Curtis, Prineha Narang, Victor Galitski
The interplay between disorder and quantum interference leads to a wide variety of physical phenomena including celebrated Anderson localization -- the complete absence of diffusive transport due to quantum interference between different particle trajectories. In two dimensions, any amount of disorder is thought to induce localization of all states at long enough length scales, though this may be prevented if bands are topological or have strong spin-orbit coupling. In this note, we present a simple argument providing another mechanism for disrupting localization: by tuning the underlying curvature of the manifold on which diffusion takes place. We show that negative curvature manifolds contain a natural infrared cut off for the probability of self returning paths. We provide explicit calculations of the Cooperon -- directly related to the weak-localization corrections to the conductivity -- in hyperbolic space. It is shown that constant negative curvature leads to a rapid growth in the number of available trajectories a particle can coherently traverse in a given time, reducing the importance of interference effects and restoring classical diffusive behavior even in the absence of inelastic collisions. We conclude by arguing that this result may be amenable to experimental verification through the use of quantum simulators.