Abstract:We report the experimental detection of bulk topological invariants in nonunitary discrete-time quantum walks with single photons. The nonunitarity of the quantum dynamics is enforced by periodically performing partial measurements on the polarization of the walker photon, which effectively introduces loss to the dynamics. The topological invariant of the nonunitary quantum walk is manifested in the quantized average displacement of the walker, which is probed by monitoring the photon loss. We confirm the topo… Show more
“…The coin operator R is implemented by a set of HWPs. The shift operator S 1 (S 2 ) is implemented by a BD [12][13][14][15]. The mode-selective loss operator M E is implemented by a PPBS.…”
Bulk-boundary correspondence, a central principle in topological matter relating bulk topological invariants to edge states, breaks down in a generic class of non-Hermitian systems that have so far eluded experimental effort. Here we theoretically predict and experimentally observe non-Hermitian bulk-boundary correspondence, a fundamental generalization of the conventional bulk-boundary correspondence, in discrete-time non-unitary quantum-walk dynamics of single photons. We experimentally demonstrate photon localizations near boundaries even in the absence of topological edge states, thus confirming the non-Hermitian skin effect. Facilitated by our experimental scheme of edge-state reconstruction, we directly measure topological edge states, which match excellently with non-Bloch topological invariants calculated from localized bulk-state wave functions. Our work unequivocally establishes the non-Hermitian bulk-boundary correspondence as a general principle underlying non-Hermitian topological systems, and paves the way for a complete understanding of topological matter in open systems.
“…The coin operator R is implemented by a set of HWPs. The shift operator S 1 (S 2 ) is implemented by a BD [12][13][14][15]. The mode-selective loss operator M E is implemented by a PPBS.…”
Bulk-boundary correspondence, a central principle in topological matter relating bulk topological invariants to edge states, breaks down in a generic class of non-Hermitian systems that have so far eluded experimental effort. Here we theoretically predict and experimentally observe non-Hermitian bulk-boundary correspondence, a fundamental generalization of the conventional bulk-boundary correspondence, in discrete-time non-unitary quantum-walk dynamics of single photons. We experimentally demonstrate photon localizations near boundaries even in the absence of topological edge states, thus confirming the non-Hermitian skin effect. Facilitated by our experimental scheme of edge-state reconstruction, we directly measure topological edge states, which match excellently with non-Bloch topological invariants calculated from localized bulk-state wave functions. Our work unequivocally establishes the non-Hermitian bulk-boundary correspondence as a general principle underlying non-Hermitian topological systems, and paves the way for a complete understanding of topological matter in open systems.
“…The dynamic coin operation implemented with a fast-switching electro-optic modulator (EOM) makes it suitable for a wide range of experiments, including the investigation of topological phenomena [22,58]. Previous photonic implementations allowed for accessing topological invariants associated with probability distributions or amplitudes within a certain step of the walk [9,22,[65][66][67][68][69]. However, topological properties can also manifest themselves in the emergence of eigenstates with associated eigenvalues that are revealed by the phase relation between the walker's wavefunctions for two consecutive steps.…”
We study topological phenomena of quantum walks by implementing a novel protocol that extends the range of accessible properties to the eigenvalues of the walk operator. To this end, we experimentally realise for the first time a split-step quantum walk with decoupling, which allows for investigating the effect of a bulk-boundary while realising only a single bulk configuration. The experimental platform is implemented with the well-established time-multiplexing architecture based on fibre-loops and coherent input states. The symmetry protected edge states are approximated with high similarities and we read-out the phase relative to a reference for all modes. In this way we observe eigenvalues which are distinguished by the presence or absence of sign flips between steps. Furthermore, the results show that investigating a bulk-boundary with a single bulk is experimentally feasible when decoupling the walk beforehand.
“…where the integer j represent sites of the walker in the 1D line. The implementations of DTQW have been achieved in several quantum systems, such as linear optics [22][23][24][32][33][34], ion traps [35,36], and neutral atom traps [37].…”
Implementation of discrete-time quantum walk (DTQW) with superconducting qubits is difficult since on-chip superconducting qubits cannot hop between lattice sites. We propose an efficient protocol for the implementation of DTQW in circuit quantum electrodynamics (QED), in which only N +1 qutrits and N assistant cavities are needed for an N -step DTQW. The operation of each DTQW step is very quick because only resonant processes are adopted. The numerical simulations show that high-similarity DTQW with the number of step up to 20 is feasible with present-day circuit QED technique. This protocol can help to study properties and applications of large-step DTQW in experiments, which is important for the development of quantum computation and quantum simulation in circuit QED.
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