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Exploration of nontrivial superconductivity and electronic band topology is at the core of condensed matter physics and applications to quantum information. The transition-metal dichalcogenide (TMDC) MoTe$_2$ has been proposed as an ideal candidate to explore the interplay between topology and superconductivity, but their studies remain limited because of the high-pressure environments required to control the topological phase transition. In this work, we demonstrate the tunable superconductivity and the resultant higher-order topology of MoTe$_2$ under extreme pressure. In the pressured T$_d$ phase, Andreev reflection spectroscopy reveals two-gap features, indicating that the Weyl fermions lead to a topological $s^{\pm}$-wave multigap superconductivity. On the other hand, the high-pressure 1T$'$ phase presents $p$-wave surface superconductivity emergent from the second-order topological bands via the bulk-to-surface proximity effect. Our analysis suggests that the topological hinge states generated from second-order topological bands evolve into zero-energy Majorana hinge states in the second-order topological superconductor. These results demonstrate the potential realization of topological superconductivity in MoTe$_2$, thus opening a pathway for studying various topological natures of TMDC materials.

Microwave quantum illumination with entangled pairs of microwave signal and optical idler modes, can achieve the sub-optimal performance with joint measurement of the signal and idler modes. Here, we first propose a testbed of microwave quantum illumination with an optical memory which is simulated with a delay line in the idler mode. It provides how much an input two-mode squeezing is necessary to compensate the loss of the optical memory, while maintaining quantum advantage over coherent state. When the memory is lossy, the input two-mode squeezing has to be higher through high cooperativity in the optical mode. Under the testbed, we propose a single-mode phase conjugate receiver that consists of a low-reflectivity beam splitter, an electro-optomechanical phase conjugator, and a photon number resolving detector. The performance of the newly proposed receiver approaches the maximum quantum advantage for local measurement. Furthermore, the quantum advantage is obtained even with an on-off detection while being robust against the loss of the memory., Comment: 8 pages, 7 figures

The thermal conductivity of heavy-fermion superconductor CeCoIn$_5$ was measured with a magnetic field rotating in the tetragonal a-b plane, with the heat current in the anti-nodal direction, $J$ || [100]. We observe a sharp resonance in thermal conductivity for the magnetic field at an angle $\theta$ $\sim$ 12$^{\circ}$, measured from the heat current direction [100]. This resonance corresponds to the reported resonance at an angle $\theta'$ $\sim$ 33$^{\circ}$ from the direction of the heat current applied along the nodal direction, $J$ || [110]. Both resonances, therefore, occur when the magnetic field is applied in the same crystallographic orientation in the two experiments, regardless of the direction of the heat current, proving conclusively that these resonances are due to the structure of the Fermi surface of CeCoIn$_5$. We argue that the uncondensed Landau quasiparticles, emerging with field, are responsible for the observed resonance. We support our experimental results with density-functional-theory model calculations of the density of states in a rotating magnetic field. Our calculations, using a model Fermi surface of CeCoIn$_5$, reveal several sharp peaks as a function of the field direction. Our study demonstrates that the thermal-conductivity measurement in rotating magnetic field can probe the normal parts of the Fermi surface deep inside the superconducting state.

Quantum illumination is to discern the presence or absence of a low reflectivity target, where the error probability decays exponentially in the number of copies used. When the target reflectivity is small so that it is hard to distinguish target presence or absence, the exponential decay constant falls into a class of objects called monotone metrics. We evaluate monotone metrics restricted to Gaussian states in terms of first-order moments and covariance matrix. Under the assumption of a low reflectivity target, we explicitly derive analytic formulae for decay constant of an arbitrary Gaussian input state. Especially, in the limit of large background noise and low reflectivity, there is no need of symplectic diagonalization which usually complicates the computation of decay constants. First, we show that two-mode squeezed vacuum (TMSV) states are the optimal probe among pure Gaussian states with fixed signal mean photon number. Second, as an alternative to preparing TMSV states with high mean photon number, we show that preparing a TMSV state with low mean photon number and displacing the signal mode is a more experimentally feasible setup without degrading the performance that much. Third, we show that it is of utmost importance to prepare an efficient idler memory to beat coherent states and provide analytic bounds on the idler memory transmittivity in terms of signal power, background noise, and idler memory noise. Finally, we identify the region of physically possible correlations between the signal and idler modes that can beat coherent states., Comment: 16 pages, 6 figures

It is important to find feasible measurement bounds for quantum information protocols. We present analytic bounds for quantum illumination with Gaussian states when using an on-off detection or a photon number resolving (PNR) detection, where its performance is evaluated with signal-to-noise ratio. First, for coincidence counting measurement, the best performance is given by the two-mode squeezed vacuum (TMSV) state which outperforms the coherent state and the classically correlated thermal (CCT) state. However, the coherent state can beat the TMSV state with increasing signal mean photon number in the case of the on-off detection. Second, the performance is enhanced by taking Fisher information approach of all counting probabilities including non-detection events. In the Fisher information approach, the TMSV state still presents the best performance but the CCT state can beat the TMSV state with increasing signal mean photon number in the case of the on-off detection. Furthermore, we show that it is useful to take the PNR detection on the signal mode and the on-off detection on the idler mode, which reaches similar performance of using PNR detections on both modes., Comment: 7+1 pages, 3 figures, close to the published version

In this paper, we propose a novel quantum-secured single-pixel imaging method that utilizes non-classical correlations of a photon pair. Our method can detect any attempts to deceive it by exploiting a non-classical correlation of photon pairs while rejecting strong chaotic light illumination through photon heralding. A security analysis based on polarization-correlation has been conducted, demonstrating that our method has improved security compared to existing quantum-secured imaging. More specifically, a partial deceiving attack, which sends a mixture of a true and a false signal, can be detected with our proposed analysis, while currently employed methods cannot. We also provide proof-of-principle demonstrations of our method and trustworthy images reconstructed using our security analysis. Our method can be developed using matured techniques used in quantum secure communication, thus offering a promising direction for practical applications in secure imaging., Comment: 11 pages, 7 figures

Two-mode squeezed vacuum states are a crucial component of quantum technologies. In the microwave domain, they can be produced by Josephson ring modulator which acts as a three-wave mixing non-degenerate parametric amplifier. Here, we solve the master equation of three bosonic modes describing the Josephson ring modulator with a novel numerical method to compute squeezing of output fields and gain at low signal power. We show that the third-order interaction from the three-wave mixing process intrinsically limits squeezing and reduces gain. Since our results are related to other general cavity-based three-wave mixing processes, these imply that any non-degenerate parametric amplifier will have an intrinsic squeezing limit in the output fields., Comment: 6+6 pages, 4 figures

We present a method to classically enhance noise-robustness of single-pixel imaging in photon counting regime with a pulsed source. By using time-domain cross-correlations between temporal profiles of a pulsed source and received signals, our scheme classically imitates the noise rejection concept of quantum imaging. Under a strong noise environment in which the background noise intensity is up to 120 times higher than the signal one, we compare three different images obtained by conventional, quantum-enhanced, and classically enhanced schemes. The results show that the classically enhanced scheme can be remarkably robust against noise in image formation, which is comparable to the quantum scheme., Comment: 10 pages, 6 figures

Imaging with non-classically correlated photon-pairs takes advantages over classical limits in terms of sensitivity and signal-to-noise ratio. However, it is still a challenge to achieve a strong resilience to background noise and losses for practical applications. In this work, we present heralded single-pixel imaging that is remarkably robust against bright background noise and severe signal losses. Using a strong temporal correlation between a photon-pair and joint measurement-based imaging method, we achieve the suppression of noise up to 1000 times larger than the signal and also demonstrate the correlation-induced SNR enhancement factor of over 200 against 70 times larger noise and a 90% signal loss compared to non-time-gated classical imaging. Our work enables correlated imaging with a highly scalable photon capacity., Comment: 6 pages, 5 figure, accepted in APL

We propose observable bounds for Gaussian illumination to maximize the signal-to-noise ratio, which minimizes the discrimination error between the presence and absence of a low-reflectivity target using Gaussian states. The observable bounds are achieved with mode-by-mode measurements. In the quantum regime using a two-mode squeezed vacuum state, our observable receiver outperforms the other feasible receivers whereas it cannot approach the quantum Chernoff bound. The corresponding observable cannot be implemented with heterodyne detections due to the additional vacuum noise. In the classical regime using a thermal state, a receiver implemented with a photon number difference measurement approaches its bound regardless of the signal mean photon number, while it asymptotically approaches the classical bound in the limit of a huge idler mean photon number., Comment: 8 pages, 8 figures, close to the published version

We propose Gaussian quantum illumination(QI) protocol exploiting asymmetrically squeezed two-mode(ASTM) state that is generated by applying single-mode squeezing operations on each mode of an initial two-mode squeezed vacuum(TMSV) state, in order to overcome the limited brightness of a TMSV state. We show that the performance of the optimal receiver is enhanced by local squeezing operation on a signal mode whereas the performance of a realistic receiver can be enhanced by local squeezing operations on both input modes. Under a fixed mean photon number of the signal mode, the ASTM state can be close to the TMSV state in the performance of QI while there is a threshold of beating classical illumination in the mean photon number of the initial TMSV state. We also verify that quantum discord cannot be a resource of quantum advantage in the Gaussian QI using the ASTM state, which is a counterexample of a previous claim., Comment: 12 pages, 8 figures; Comments are welcome

In recent development of quantum technologies, a frequency conversion of quantum signals has been studied widely. We investigate the optic-microwave entanglement that is generated by applying an electro-optomechanical frequency conversion scheme to one mode in an optical two-mode squeezed vacuum state. We quantify entanglement of the converted two-mode Gaussian state, where surviving entanglement of the state is analyzed with respect to the parameters of the electro-optomechanical system. Furthermore, we show that there exists an upper bound for the entanglement that survives after the conversion of highly entangled optical states. Our study provides a theoretical platform for a practical quantum illumination system., Comment: 9 pages, 3 figures

The $d$-wave superconductor $\mathrm{CeCoIn_5}$ has been proposed as a strong candidate for supporting the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state near the low-temperature boundary of its upper critical field. Neutron diffraction, however, finds spin-density-wave (SDW) order in this part of the phase diagram for field in the $a$-$b$ plane, and evidence for the SDW disappears as the applied field is rotated toward the tetragonal $c$ axis. It is important to understand the interplay between the SDW and a possible FFLO state in $\mathrm{CeCoIn_5}$, as the mere existence of an SDW does not necessary exclude an FFLO state. Here, based on a model constructed on the basis of available experiments, we show that an FFLO state competes with an SDW phase. The SDW state in $\mathrm{CeCoIn_5}$ is stabilized when the field is directed close to the $a$-$b$ plane. When the field is rotated toward the $c$ axis, the FFLO state emerges, and the SDW phase disappears. In the FFLO state, the nodal planes with extra quasiparticles (where the superconducting order parameter is zero) are perpendicular to the field, and in the SDW phase, the quasiparticle density of states is reduced. We test this model prediction by measuring heat transported by normal quasiparticles in the superconducting state. As a function of field, we observe a reduction of thermal conductivity for field close to the $a$-$b$ plane and an enhancement of thermal conductivity when field is close to the $c$ axis, consistent with theoretical expectations. Our modeling and experiments, therefore, indicate the existence of the FFLO state when field is parallel to the $c$ axis., Comment: 5 pages and 4 figures

The ordering wave vector $\mathbf{Q}$ of a spin density wave (SDW), stabilized within the superconducting state of $\mathrm{CeCoIn_5}$ in a high magnetic field, has been shown to be hypersensitive to the direction of the field. $\mathbf{Q}$ can be switched from a nodal direction of the $d$-wave superconducting order parameter to a perpendicular node by rotating the in-plane magnetic field through the antinodal direction within a fraction of a degree. Here, we address the dynamics of the switching of $\mathbf{Q}$. We use a free energy functional based on the magnetization density, which describes the condensation of magnetic fluctuations of nodal quasiparticles, and show that the switching process includes closing of the SDW gap at one $\mathbf{Q}$ and then reopening the SDW gap at another $\mathbf{Q}$ perpendicular to the first one. The magnetic field couples to $\mathbf{Q}$ through the spin-orbit interaction. Our calculations show that the width of the hysteretic region of switching depends linearly on the deviation of magnetic field from the critical field associated with the SDW transition, consistent with our thermal conductivity measurements. The agreement between theory and experiment supports our scenario of the hypersensitivity of the $Q$ phase on the direction of magnetic field, as well as the magnon condensation as the origin of the SDW phase in $\mathrm{CeCoIn_5}$.

The appearance of spin-density-wave (SDW) magnetic order in the low-temperature and high-field corner of the superconducting phase diagram of CeCoIn$_5$ is unique among unconventional superconductors. The nature of this magnetic $Q$ phase is a matter of current debate. Here, we present the thermal conductivity of CeCoIn$_5$ in a rotating magnetic field, which reveals the presence of an additional order inside the $Q$ phase that is intimately intertwined with the superconducting $d$-wave and SDW orders. A discontinuous change of the thermal conductivity within the $Q$ phase, when the magnetic field is rotated about antinodes of the superconducting $d$-wave order parameter, demands that the additional order must change abruptly together with the recently observed switching of the SDW. A combination of interactions, where spin-orbit coupling orients the SDW, which then selects the secondary $p$-wave pair-density-wave component (with an average amplitude of 20\% of the primary $d$-wave order parameter), accounts for the observed behavior.

The quantum anomalous Hall (QAH) effect is predicted to possess, at zero magnetic field, chiral edge channels that conduct spin polarized current without dissipation. While edge channels have been observed in previous experimental studies of the QAH effect, their dissipationless nature at a zero magnetic field has not been convincingly demonstrated. By a comprehensive experimental study of the gate and temperature dependences of local and nonlocal magnetoresistance, we unambiguously establish the dissipationless edge transport. By studying the onset of dissipation, we also identify the origin of dissipative channels and clarify the surprising observation that the critical temperature of the QAH effect is two orders of magnitude smaller than the Curie temperature of ferromagnetism., Comment: main text+supporting materials. This is the accepted version for PRL. Comments are welcome

The discovery of the quantum Hall (QH) effect led to the realization of a topological electronic state with dissipationless currents circulating in one direction along the edge of a two dimensional electron layer under a strong magnetic field. The quantum anomalous Hall (QAH) effect shares a similar physical phenomenon as the QH effect, whereas its physical origin relies on the intrinsic spin-orbit coupling and ferromagnetism.Here we report the experimental observation of the QAH state in V-doped (Bi,Sb)2Te3 films with the zero-field longitudinal resistance down to 0.00013+-0.00007h/e2 (~3.35+-1.76 ohm), Hall conductance reaching 0.9998+-0.0006e2/h and the Hall angle becoming as high as 89.993+-0.004degree at T=25mK. Further advantage of this system comes from the fact that it is a hard ferromagnet with a large coercive field (Hc>1.0T) and a relative high Curie temperature. This realization of robust QAH state in hard FMTIs is a major step towards dissipationless electronic applications without external fields., Comment: 16 pages, 4 figures, this is the final version, accepted by Nature Materials, forthcoming

The resonant period drop observed at low temperatures in torsional oscillators containing solid helium had been interpreted as a signature of supersolid. However, it was found that the shear modulus increase found in solid helium at the same low temperature could also decrease the resonant period of the torsional oscillator. We report the results of a study in two different torsional oscillators that were specially designed to minimize the shear modulus effect and maximize any possible supersolid response. We were able to place an upper limit on the nonclassical rotational inertia or supersolid fraction of $4\times10^{-6}$. Moreover, we have repeated an earlier experiment on hcp $^3$He solid, which shows similar low temperature stiffening as in hcp $^4$He. We found that the small drop of the resonant period measured in the hcp $^3$He sample is comparable in size to that found in the hcp $^4$He samples. These results strongly suggest that the resonant period drop reported in most torsional oscillator studies in the last decade is primarily a consequence of the shear modulus stiffening effect.

In 2004, Kim and Chan (KC) carried out torsional oscillator (TO) measurements of solid helium confined in porous Vycor glass and found an abrupt drop in the resonant period below 200 mK. The period drop was interpreted as probable experimental evidence of nonclassical rotational inertia (NCRI). This experiment sparked considerable activities in the studies of superfluidity in solid helium. More recent ultrasound and TO studies, however, found evidence that shear modulus stiffening is responsible for at least a fraction of the period drop found in bulk solid helium samples. The experimental configuration of KC makes it unavoidable to have a small amount of bulk solid inside the torsion cell containing the Vycor disc. We report here the results of a new helium in Vycor experiment with a design that is completely free from any bulk solid shear modulus stiffening effect. We found no measureable period drop that can be attributed to NCRI.