We demonstrate symmetry protected bundle emission in the cavity QED system under the ultrastrong coupling regime. Parity symmetry of Rabi model only permits the super-Rabi oscillations with periodic generation of even photons in cavity, which is realized by the laser driven flip of qubit and the parity conserved transitions induced by Rabi interaction. Combined with dissipation, only 2$n$-photon correlated emissions are allowed, and the corresponding purities are significantly enhanced by the parity symmetry, due to the almost perfect suppression of bundle emissions with odd correlated photons. The switching of bundle emissions between even and odd correlated photons can be controlled by manipulating the parity symmetry of system with an added magnetic field. This work extends multi-photon bundle emission to the ultrastrong coupling regime, and offers the prospect of exploring symmetry-protected multi-quanta physics.
We develop a general theoretical framework to dynamically engineer quantum correlations in the frequency-comb emission from an array of superconducting qubits in a waveguide, rigorously accounting for the temporal modulation of the qubit resonance frequencies. We demonstrate, that when the resonance frequencies of the two qubits are periodically modulated with a $π$ phase shift, it is possible to realize simultaneous bunching and antibunching in cross-correlations of the scattered photons from different sidebands. Our approach, based on the dynamical conversion between the quantum excitations …
Qubits constructed from uncoupled Majorana fermions are protected from decoherence, but to perform a quantum computation this topological protection needs to be broken. Parity-protected quantum computation breaks the protection in a minimally invasive way, by coupling directly to the fermion parity of the system --- irrespective of any quasiparticle excitations. Here we propose to use a superconducting charge qubit in a transmission line resonator (a socalled transmon) to perform parity-protected rotations and read-out of a topological (top) qubit. The advantage over an earlier proposal using …
High fidelity quantum information processing requires a combination of fast gates and long-lived quantum memories. In this work, we propose a hybrid architecture, where a parity-protected superconducting qubit is directly coupled to a Majorana qubit, which plays the role of a quantum memory. The superconducting qubit is based upon a $π$-periodic Josephson junction realized with gate-tunable semiconducting wires, where the tunneling of individual Cooper pairs is suppressed. One of the wires additionally contains four Majorana zero modes that define a qubit. We demonstrate that this enables the …
Open, non-equilibrium systems with balanced gain and loss, known as parity-time ($\mathcal{PT}$)-symmetric systems, exhibit properties that are absent in closed, isolated systems. A key property is the $\mathcal{PT}$-symmetry breaking transition, which occurs when the gain-loss strength, a measure of the openness of the system, exceeds the intrinsic energy-scale of the system. We analyze the fate of this transition in disordered lattices with non-Hermitian gain and loss potentials $\pm iγ$ at reflection-symmetric sites. Contrary to the popular belief, we show that the $\mathcal{PT}$-symmetric …
We have developed and characterized a symmetry-protected superconducting qubit that offers simultaneous exponential suppression of energy decay from charge and flux noise, and dephasing from flux noise. The qubit consists of a Cooper-pair box (CPB) shunted by a superinductor, thus forming a superconducting loop. Provided the offset charge on the CPB island is an odd number of electrons, the qubit potential corresponds to that of a $\cos ϕ/ 2$ Josephson element, preserving the parity of fluxons in the loop via Aharonov-Casher interference. In this regime, the logical-state wavefunctions reside …
The aim of quantum metrology is to estimate target parameters as precisely as possible. In this paper, we consider quantum metrology based on symmetry-protected adiabatic transformation. We introduce a ferromagnetic Ising model with a transverse field as a probe and consider the estimation of a longitudinal field. Without the transverse field, the ground state of the probe is given by the Greenberger-Horne-Zeilinger state, and thus the Heisenberg limit estimation of the longitudinal field can be achieved through parity measurement. In our scheme, full information of the longitudinal field enco…
Exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, and parity-time ($\mathcal{PT}$) symmetry, reflecting balanced gain and loss in photonic systems, are paramount concepts in non-Hermitian systems. We here complete the topological classification of exceptional nodal degeneracies protected by $\mathcal{PT}$ symmetry in up to three dimensions and provide simple example models whose exceptional nodal topologies include previously overlooked possibilities such as second-order knotted surfaces of arbitrary genus, third-order knots and fourth-order points.
Symmetry plays fundamental role in physics and the nature of symmetry changes in non-Hermitian physics. Here the symmetry-protected scattering in non-Hermitian linear systems is investigated by employing the discrete symmetries that classify the random matrices. The even-parity symmetries impose strict constraints on the scattering coefficients: the time-reversal (C and K) symmetries protect the symmetric transmission or reflection; the pseudo-Hermiticity (Q symmetry) or the inversion (P) symmetry protects the symmetric transmission and reflection. For the inversion-combined time-reversal symm…
We compute the effect of Markovian bulk dephasing noise on the staggered magnetization of the spin-1/2 XXZ Heisenberg chain, as the system evolves after a Néel quench. For sufficiently weak system-bath coupling, the unitary dynamics are found to be preserved up to a single exponential damping factor. This is a consequence of the interplay between $\mathbb{PT}$ symmetry and weak symmetries, which strengthens previous predictions for $\mathbb{PT}$-symmetric Liouvillian dynamics. Requirements are a non-degenerate $\mathbb{PT}$-symmetric generator of time evolution $\hat{\mathcal{L}}$, a weak pari…
Topological phases of bosons with local parity coupling on a dimerized lattice
Univ. Toulouse, CNRS, Laboratoire de Physique Théorique（图卢兹大学，法国国家科学研究中心，理论物理实验室）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）
We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. Here, the spatial symmetries of the one-dimensional lattice are considered together with an additional 'vertical reflection', which we take to be an on-site $\mathbb{Z}_2$ symmetry. We identify seventeen distinct non-trivial phases, define canonical forms, and compare the topological indices obtained from the MPS analysis with the group cohomological predictions. We furthermore construct explicit renormalizati…
{\it We first give a geometrical description of the action of the parity operator ($\hat{P}$) on non relativistic spin ${{1}\over{2}}$ Pauli spinors in terms of bundle theory. The relevant bundle, $SU(2)\odot \Z_2\to O(3)$, is a non trivial extension of the universal covering group $SU(2)\to SO(3)$. $\hat{P}$ is the non relativistic limit of the corresponding Dirac matrix operator ${\cal P}=iγ_0$ and obeys $\hat{P}^2=-1$. Then, from the direct product of O(3) by $\Z_2$, naturally induced by the structure of the galilean group, we identify, in its double cover, the time reversal operator ($\hat…
We show how angular momentum conservation can stabilise a symmetry-protected quasi-topological phase of matter supporting Majorana quasi-particles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated b…
We construct exactly solved commuting projector Hamiltonian lattice models for all known 2+1d fermionic symmetry protected topological phases (SPTs) with on-site unitary symmetry group $G_f = G \times \mathbb{Z}_2^f$, where $G$ is finite and $\mathbb{Z}_2^f$ is the fermion parity symmetry. In particular, our models transcend the class of group supercohomology models, which realize some, but not all, fermionic SPTs in 2+1d. A natural ingredient in our construction is a discrete form of the spin structure of the 2d spatial surface $M$ on which our model is defined, namely a `Kasteleyn' orientati…
Periodically driven quantum systems, known as Floquet systems, have been a focus of non-equilibrium physics in recent years, thanks to their rich dynamics. Not only time-periodic systems exhibit symmetries similar to those in spatially periodic systems, but they also display novel behavior due to symmetry breaking. Characterizing such dynamical symmetries is crucial, but the task is often challenging, due to limited driving strength and the lack of an experimentally accessible characterization protocol. Here, we show how to characterize dynamical symmetries including parity, rotation, and part…
Topological qubits based on $SU(N)$-symmetric valence-bond solid models are constructed. A logical topological qubit is the ground subspace with two-fold degeneracy, which is due to the spontaneous breaking of a global parity symmetry. A logical $Z$-rotation by angle $\frac{2π}{N}$, for any integer $N > 2$, is provided by a global twist operation, which is of topological nature and protected by the energy gap. A general concatenation scheme with standard quantum error-correction codes is also proposed, which can lead to better codes. Generic error-correction properties of symmetry-protected to…
We show how 1+1-dimensional fermionic symmetry-protected topological states (SPTs, i.e. nontrivial short-range entangled gapped phases of quantum matter whose boundary exhibits 't Hooft anomaly and whose bulk cannot be deformed into a trivial tensor product state under finite-depth local unitary transformations only in the presence of global symmetries), indeed can be unwound to a trivial state by enlarging the Hilbert space via adding extra degrees of freedom and suitably extending the global symmetries. The extended projective global symmetry on the boundary can become supersymmetric in a sp…
We present a new hardware-efficient paradigm for universal quantum computation which is based on encoding, protecting and manipulating quantum information in a quantum harmonic oscillator. This proposal exploits multi-photon driven dissipative processes to encode quantum information in logical bases composed of Schrödinger cat states. More precisely, we consider two schemes. In a first scheme, a two-photon driven dissipative process is used to stabilize a logical qubit basis of two-component Schrödinger cat states. While such a scheme ensures a protection of the logical qubit against the photo…
