Abstract
We experimentally study quantum Zeno effects in a paritytime (PT) symmetric cold atom gas periodically coupled to a reservoir. Based on the stateoftheart control of intersite couplings of atoms in a momentum lattice, we implement a synthetic twolevel system with passive PT symmetry over two lattice sites, where an effective dissipation is introduced through repeated couplings to the rest of the lattice. Quantum Zeno (antiZeno) effects manifest in our experiment as the overall dissipation of the twolevel system becoming suppressed (enhanced) with increasing coupling intensity or frequency. We demonstrate that quantum Zeno regimes exist in the broken PT symmetry phase, and are bounded by exceptional points separating the PT symmetric and PT broken phases, as well as by a discrete set of critical coupling frequencies. Our experiment establishes the connection between PTsymmetrybreaking transitions and quantum Zeno effects, and is extendable to higher dimensions or to interacting regimes, thanks to the flexible control with atoms in a momentum lattice.
Introduction
Coherent evolution of a quantum system can be frozen when frequently interrupted by measurements or perturbations. Such a phenomenon, famed as the quantum Zeno effect, has been experimentally observed in various physical systems^{1,2,3,4,5}, and has found widespread utilities in quantum information^{6,7,8,9,10,11,12,13,14,15,16} and quantum simulation^{17,18,19,20,21}. In a complementary fashion, with an appropriate repetition rate of measurements, the evolution of the system can also be accelerated under what is known as the antiZeno effect^{22}. Intriguingly, both quantum Zeno and antiZeno effects are alternatively accessible through continuous strong couplings or fast unitary kicks^{3,17,23} that couple a system to an auxiliary Hilbert space. With the auxiliary Hilbert space playing the role of environment, these processes give rise to dissipative systemreservoir couplings, under which the time evolution of the system is effectively driven by a nonHermitian Hamiltonian. Since a dissipative system under nonunitary evolution driven by a nonHermitian Hamiltonian is not normpreserving and necessarily decays, the quantum (anti)Zeno effects therein manifest as the suppression (enhancement) of decay.
Although evidence of quantum Zeno effects have been theoretically demonstrated and experimentally observed in nonHermitian settings^{24,25}, surprisingly little is discussed on its interplay with paritytime (PT) symmetry, despite the latter being a ubiquitous property of nonHermitian systems while holding great promise for future applications^{26,27,28}. A PT symmetric, nonHermitian system possesses two distinct phases: the paritytime symmetric (PTS) phase, with entirely real eigenenergy spectrum; and the paritytime broken (PTB) phase, where eigenenergies are complex in general. The two phases are separated by exceptional points, with coalescing eigenstates and eigenenergies. While quantum Zeno effects naturally emerge in the deep PTB regime that can be mapped to an open system possessing continuous and strong coupling with a dissipative reservoir^{29}, the fate of quantum Zeno (antiZeno) effects is less well known in the PTS regime or near exceptional points, both of which typically occur at much smaller dissipation strengths^{29,30,31}. A very recent theoretical study shows that exceptional points of a PT symmetric Hamiltonian also mark the boundary between quantum Zeno and antiZeno regimes^{32}, suggesting a deep connection between the two previously independent fields of study. Here we experimentally confirm such a connection in a PT symmetric, synthetic twolevel system, embedded in a momentum lattice of cold atoms.
Results
PT symmetry breaking transitions in a dissipative twolevel system
We focus on a twolevel system under timeperiodic dissipation^{32}, as illustrated in Fig. 1a. The timedependent Hamiltonian is
where \({\mathbb{I}}\) and σ_{x,z} are the identity and Pauli matrices respectively, τ is the evolution time, and t is the interstate coupling rate. The timeperiodic dissipation rate γ is given by
where \(j\in {\mathbb{Z}}\), the modulation period T = 2π/Ω with Ω the modulation frequency, γ_{0} characterizes the modulation intensity, and τ_{0} is the duty time interval with nonzero γ in each cycle; see Fig. 1b.
Hamiltonian (1) is passive PT symmetric, in that it is purely dissipative, but is directly related to the standard PT symmetric Hamiltonian \(\hbar{\epsilon_{\pm}}\) with balanced gain and loss. Explicitly, \({\mathcal{PT}}{H}_{PT}{{\mathcal{PT}}}^{1}={H}_{PT}\), with the PT symmetry operator \({\mathcal{PT}}={\sigma }_{x}{\mathcal{K}}\) where \({\mathcal{K}}\) is complex conjugation. Since PT symmetry of H is determined by the imaginary parts of the quasienergies \(\hslash{\epsilon_{\pm}}\) of the corresponding Floquet Hamiltonian^{31,32}, we adopt a dimensionless parameter \(\lambda = {\rm{Im}}({\epsilon }_{+}{\epsilon }_{}) /t\) to characterize the PTsymmetry breaking transition. Here \({e}^{i{\epsilon }_{\pm }T/\hslash }\) are eigenvalues of the nonunitary timeevolution operator \(U={\mathcal{T}}{e}^{i\mathop{\int}\nolimits_{0}^{T}H(\tau )/\hslash d\tau }\), where \({\mathcal{T}}\) is the timeordering operator. For λ = 0, the system lies in the PTS phase, while λ > 0 corresponds to a PTB phase.
Figure 1c shows a numerically calculated phase diagram with a fixed τ_{0}t. The white PTS region is separated into several blocks (marked as \({{\mathcal{M}}}_{j}\)), by a series of critical modulation frequencies Ω_{j} = 2t/j (\(j\in {{\mathbb{N}}}^{+}\)) at which the PTS phase vanishes and PTsymmetry breaking is at its maximum. The colored PTB regimes are further divided by the critical modulation frequencies into \({{\mathcal{L}}}_{j}\) and \({{\mathcal{V}}}_{j}\) regions, respectively, corresponding to quantum Zeno and antiZeno regimes, as we explicitly demonstrate later. For any fixed Ω ≠ Ω_{j}, a PTS to PTB transition (\({{\mathcal{M}}}_{j}\to {{\mathcal{L}}}_{j}\) or \({{\mathcal{M}}}_{j}\to {{\mathcal{V}}}_{j+1}\)) is crossed when increasing γ_{0} from weak to strong. However, for a fixed γ_{0}, the PTS and PTB phases alternate (\({{\mathcal{M}}}_{j}\to {{\mathcal{L}}}_{j}\to {{\mathcal{V}}}_{j}\to {{\mathcal{M}}}_{j1}\to {{\mathcal{L}}}_{j1}\to \cdots\)) with increasing modulation frequency Ω. While the phase diagram is distinct from that of PT symmetric systems under a continuous dissipation^{29}, a crucial observation is that quantum Zeno regimes exist in the PTB phases, and are bounded by critical frequencies, as well as by exceptional points pertaining to the PT symmetry breaking transitions.
Experimental implementation
To experimentally simulate the nonunitary dynamics driven by Hamiltonian (1), we embed the dissipative Hamiltonian (1) into a larger Hilbert space composed of atomic momentum states. As illustrated in Fig. 2a, a momentum lattice is generated by imposing multiple pairs of counterpropagating, fardetuned Bragg lasers (with the wavelength λ_{0} = 1064 nm) on a Bose–Einstein condensate (BEC) of ~10^{5}^{87}Rb atoms in a weak optical dipole trap^{33,34,35}. The frequencies of the Bragg lasers are carefully designed to couple 8 discrete momentum states \(p_{n}={2n}\hbar{k}\)(k = 2π/λ_{0} and n = 0, 1,...7), which form a synthetic lattice of finite size, with individually tunable Braggassisted tunneling strength t_{n} between adjacent sites \(\leftn1\right\rangle\) and \(\leftn\right\rangle\); see Fig. 2b, c. A unitary kick is then introduced through a squarewave modulation t_{2} = t_{z}(τ) for the intersite coupling \(\left1\right\rangle \leftrightarrow \left2\right\rangle\). Consistent with Eq. (2), t_{z}(τ) = t_{0} for jT ≤ τ < jT + τ_{0}, while vanishes for other time intervals. Treating momentumlattice sites \(\leftn\ge 2\right\rangle\) as a reservoir (within which the coupling strength t_{n>2} = t), we find that dynamics within the twodimensional subspace spanned by \(\{\left0\right\rangle ,\left1\right\rangle \}\) to be dissipative, and effectively driven by Hamiltonian (1) with \({\gamma }_{0} \sim {t}_{0}^{2}/t\)^{36}. While the above expression of γ_{0} is perturbatively valid for t_{0} ≪ t, we find it capable of capturing the dissipative properties qualitatively well at short evolution times even for t_{0} ~ t. As such, we implement an effectively dissipative twolevel system in momentum space, whose dissipation originates from unitary kicks that, with kick frequency Ω and intensity γ_{0}, periodically couple the system with a reservoir.
We study both the PT symmetry breaking transition and the quantum Zeno (antiZeno) effects through the dissipative dynamics. Specifically, we initialize the atoms in the state \(\left0\right\rangle\), and let them evolve for a short time τ_{e}, before applying a timeofflight image to record the atomic probability distribution P_{n} for each momentum lattice site, normalized by the total atom population over the momentum lattice (see Methods). Under the passive PT symmetric Hamiltonian (1), the PTS and PTB phases can be dynamically differentiated by the corrected probability^{31}
which reflects the time evolution of the squared state norm within the synthetic subspace driven by the Hamiltonian H_{PT}. It follows that (see middle panels in Fig. 3), \({{\mathcal{P}}}_{s}^{c}\) should be on the order of unity in the PTS phase, while it should exponentially grow with time in the PTB phase. To further characterize quantum Zeno and antiZeno regimes, we probe the effective loss rate \(\bar{\gamma }\) via
where \({{\mathcal{P}}}_{r}\) is the total population loss of the dissipative twolevel system during the time evolution up to τ_{e}, with \({{\mathcal{P}}}_{r}={\sum }_{n\ge 2}{P}_{n}\). As we detail in the Supplementary Information, while quantum Zeno and antiZeno effects are typically defined as the change in decay of a given unstable state rather than that of the whole system, the effective loss rate \(\bar{\gamma }\) extracted from Eq. (4) constitutes a reasonably good indicator of the quantum Zeno to antiZeno transition (as well as the PT phase transition), as long as τ_{e} is sufficiently long. While we typically fix τ_{e} to be two or three modulation periods, limited by both the finite size of the reservoir and the decoherence time of the system^{25,37}, it is already long enough to reveal the transition point in our experiment.
Quantum Zeno effect across PT phase transitions
In Fig. 3a, we show the experimentally constructed corrected probability \({{\mathcal{P}}}_{s}^{c}\) and the effective loss rate \(\bar{\gamma }\) across the PT phase transition \({{\mathcal{M}}}_{0}\to {{\mathcal{L}}}_{0}\) at a high kick frequency Ω/t = 10 and with increasing kick intensity γ_{0}. The corrected probability (middle panel) becomes exponentially large beyond the exceptional point at γ_{0}/t ~ 2 (dashdotted vertical line from upper panel). In the PTS (PTB) phase \({{\mathcal{M}}}_{0}\) (\({{\mathcal{L}}}_{0}\)), the effective loss rate of the synthetic twolevel system increases (decreases) with increasing γ_{0} (see lower panel), indicating quantum antiZeno (Zeno) regime. The effective loss rate \(\bar{\gamma }\) peaks near the exceptional point, consistent with the theoretical prediction that the quantum Zeno to antiZeno transition should coincide with the PTBPTS transition.
However, such is not the case at lower kick frequencies. As illustrated in Fig. 3b, when γ_{0} is tuned at a fixed Ω/t = 2.5, \(\bar{\gamma }\) increases monotonically across the transition \({{\mathcal{M}}}_{0}\to {{\mathcal{V}}}_{1}\) at γ_{0}/t = 2.8 (dashdotted line), suggesting both the PT symmetric \({{\mathcal{M}}}_{0}\) and the PT broken \({{\mathcal{V}}}_{1}\) belong to the quantum antiZeno regime. Note that at the critical kick frequencies, for instance Ω_{1} = 2t, \(\bar{\gamma }\) also increases with increasing γ_{0}. Thus, quantum antiZeno effects survive at the boundaries between \({{\mathcal{V}}}_{j}\) and \({{\mathcal{L}}}_{j}\) in the PTB phase.
Apart from tuning γ_{0}, both the PTsymmetry breaking transition and quantum Zeno to antiZeno transition can be crossed by changing the kick frequency, which amounts to traversing the phase diagram Fig. 1 vertically. Figure 3c shows the measured \(\bar{\gamma }\) across multiple PT phase transitions by increasing Ω with a fixed γ_{0}/t ~ 9. The measured effective loss rate \(\bar{\gamma }\) peaks near the PTsymmetry phase boundary between \({{\mathcal{M}}}_{j}\) and \({{\mathcal{L}}}_{j}\), consistent with the coincidence of the two transitions according to the theoretical phase diagram. Furthermore, a local minimum in \(\bar{\gamma }\) is found near the critical kick frequency Ω_{1} = 2t (lower panel), where a “slow mode,” i.e., the eigenstate with the smaller imaginary eigenvalue, dominates the dynamics^{32}. We emphasize that the occurrence of quantum antiZeno effect in the PTB regime is unique to slow modulations. For fast modulations (Ω/t ≫ 1, where the transition \({{\mathcal{M}}}_{0}\to {{\mathcal{L}}}_{0}\) lies), increasing the kick rate is similar to enlarging the dissipation rate in the continuous case^{23,32}. There, only a single transition point from the quantum antiZeno to Zeno regime exists, whic \(\hslash\) h occurs exactly at the exceptional point.
Experimental measurements in Fig. 3 qualitatively agree with theoretical predictions, since both the weakcoupling (i.e., the coupling strength \(\hbar t_{n}\) ≪ 8E_{r} with E_{r} = \(\hbar^{2}\)k^{2}/2m) and weakinteraction (the interaction strength much smaller compared with the \(\hbar t_{n}\)) conditions are satisfied throughout our experiments. Nevertheless, quantitative deviations exist, which mainly derive from two sources. First, the kick intensity γ_{0} in the effective Hamiltonian (1) would deviate from the perturbative expression \({\gamma }_{0} \sim {t}_{0}^{2}/t\) when either the coupling t_{0} or the evolution time becomes sufficiently large. This is the main reason for the slight discrepancy between the location of the maximum loss rate in Fig. 3a, either numerically simulated (dashed and solid lines) or experimentally measured, and that of the theoretically predicted exceptional point using the perturbative kick intensity (dashdotted). Second, highorder, nonresonant coupling terms play an important role in our experiment, as is manifest in Fig. 3 where the experimental data agree better with simulations considering the nonresonant coupling terms (solid lines). As nonresonant couplings enable the \(\left0\right\rangle \leftrightarrow \left1\right\rangle\) transition, the population of the \(\left1\right\rangle\) state leads to an underestimation of loss for a finite evolution time. Other factors, for example, interactioninduced selftrapping in the momentum lattice and the momentum broadening due to the weak trap potential^{25,37,38}, also lead to underestimations of the loss rate. These experimental imperfections lead to an overestimation of the corrected probability \({{\mathcal{P}}}_{s}^{c}\) (middle panels in Fig. 3), while the overall measured profiles still qualitatively agree with the theoretical predictions on the PT phase transition.
Correspondence between quantum (anti)Zeno effects and PT phases
Finally, we map out the phase diagram for quantum Zeno to antiZeno transition by sweeping t_{0} (hence γ_{0}) for a set of fixed Ω, and plotting the quantity \(\kappa \bar{\gamma }\) with \(\kappa ={\rm{sgn}}({{\Delta }}\bar{\gamma }/{{\Delta }}{\gamma }_{0})\); see Fig. 4. Here the difference \({{\Delta }}\bar{\gamma }/{{\Delta }}{\gamma }_{0}\) is calculated from experimental data for each fixed Ω. By definition, \(\kappa \bar{\gamma }\,<\,0\) (\(\kappa \bar{\gamma }\,>\,0\)) represents the quantum Zeno (antiZeno) regime. At the lowerright corner of Fig. 4, \(\kappa \bar{\gamma }\) is close to zero, due to a vanishing t_{z} and a disconnected reservoir. At the upperleft corner, \(\kappa \bar{\gamma }\) also approaches zero, as loss to the reservoir is suppressed, which is equivalent to the standard quantum Zeno effect in the case of continuous, strong couplings. Most importantly, by superimposing the boundaries of PT transitions (black dashed) and the critical kick frequency (blue dashed), it is clear that our measured phase diagram in Fig. 4 agrees well with the theoretical prediction in Fig. 1c, thus confirming the following correspondence
Such a relationship reveals the deep connection between PT transition and quantum Zeno effects.
However, we note that both quantum Zeno and antiZeno effects can occur in dissipative systems without PT symmetry and devoid of exceptional points^{39,40}. For instance, by considering a system with an additional diagonal detuning δσ_{z} (δ being real)^{41,42}, slowdecaying modes emerge that give rise to antiZeno effects^{40}, even in the absence of PT symmetry. Therefore, the elegant correspondence in Eq. (5) should be understood in the context of PT symmetric systems.
Discussion
To conclude, we have experimentally established the connection between the quantum Zeno effect and PT phases in a dissipative Floquet system: while the PTS phase generally leads to the quantum antiZeno effect, both quantum Zeno and antiZeno effects can occur in the PTB region. Crucially, the quantumZeno regimes are bounded by a discrete set of critical coupling frequencies, and by exceptional points. Besides shedding new lights on the relation of quantum measurements and dynamics of nonHermitian systems, our experiment also offers a new way of simulating PT physics using cold atoms, which is readily extendable to higher dimensions (see Supplementary Information). While quantum Zeno effects and the associated quantum Zeno subspace^{23} generally exist for multilevel systems, the scalability of the correspondence considered here to higher dimensions is an interesting open question that we leave to future studies.
Furthermore, the above analyses are all within the scope of singleparticle physics, without considering the effect of interactions. Specifically, manybody interactions in the momentum lattice assume the form of densitydependent, attractive onsite potentials^{38}. When the atomic density or the scattering length is large enough, atoms in momentum space exhibit the socalled interactioninduced localization^{37,38}. Since the quantum Zeno dynamics can also be regarded as a form of localization (or stabilization) within the quantum Zeno subspace^{43,44,45}, it will be interesting to study the interplay between interactions and quantum Zeno effects in future experiments^{46,47,48,49}.
Methods
Experimental settings
The ^{87}Rb BEC is prepared in an optical dipole trap. The multiple discrete momentum states are coupled with multifrequency Bragg laser pairs. The different frequency components are imprinted by two acoustic optical modulators. One shifts the frequency of the incoming beam by −100 MHz, and another shifts it by 100 MHz − ∑_{n}ν_{n}/2π (n ≥ 1) with ν_{n} = 4(2n − 1)\(\hbar\)k^{2}/2m (see the main text). As a consequence, the transition between the two momentum states, \(\leftn1\right\rangle \leftrightarrow \leftn\right\rangle\), can be resonantly triggered by the {ω_{+}, ω_{n}} laser pair.
After the system evolves for a finite time τ_{e}, we directly resolve the populations in each momentum state by letting the atoms fall freely in space for 20 ms with all lasers switched off, before the atoms are imaged by a camera. Atoms with different momenta get separated in the xdirection along which the Bragg beams are applied (see Fig. 1 in the main text). To obtain the relative populations in each state, we integrate the image in the ydirection, and then fit the data with a 10peak Gauss function, \({\mathcal{A}}(x)=\mathop{\sum }\nolimits_{n = 1}^{8}{A}_{n}\,{\text{exp}}\,\left[{\left(\frac{xnd}{a}\right)}^{2}\right]\). Normalizing the resulting amplitude \({{\mathcal{A}}}_{n}\) by \(\mathop{\sum }\nolimits_{n = 1}^{8}{{\mathcal{A}}}_{n}\), we finally get the atom population distribution on each site, P_{n}.
Effective Hamiltonian with offresonant terms
Following the theory of lightatom interaction in ref. ^{33}, we obtain the effective timedependent full Hamiltonian
with ϕ_{+} and ϕ_{i} the phases of beams with frequencies ω_{+} and ω_{i}, respectively (see Fig. 2 in the main text). We simply let ϕ_{+} = 0, and ϕ_{i} be the modulated phase relative to ϕ_{+} from the AOM. As we choose ω_{i} = ω_{+} − 4(2i − 1)\(\hbar\)k^{2}/2m, the simplified ideal model can be obtained by considering only the resonant terms, i.e., letting i = n, as
with \({t}_{n}={e}^{i{\phi }_{n}}{{{\Omega }}}_{+}{{{\Omega }}}_{n}/4 {{\Delta }}\). This gives the general tightbinding form for a momentumstate chain. If we simply treat the n ≥ 2 part as an effective reservoir, and apply the secondorder perturbation with t_{2} = t_{z} and t_{n≠2} = t, the loss rate of site \(\left1\right\rangle\) should approximately be \({\gamma }_{0} \sim {t}_{z}^{2}/t\)^{36}. Then we obtain the dissipative twolevel Hamiltonian in the main text.
Clearly, the ℓthorder nonresonant terms, responsible for the transition \(\leftn1\right\rangle \leftrightarrow \leftn\right\rangle\), can be induced by {ω_{+}, ω_{n−ℓ}} and {ω_{+}, ω_{n+ℓ}} laser pairs with detunings of ∓8ℓ\(\hslash\)k^{2}/2m, respectively. These terms are given by
leading the full Hamiltonian H_{eff} = ∑_{ℓ}H^{(ℓ)}. In our experiment, 8\(\hbar\)k^{2}/2m corresponds to ~2π × 16.2 kHz.
Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
References
Itano, W. M., Heinzen, D. J., Bollinger, J. J. & Wineland, D. J. Quantum Zeno effect. Phys. Rev. A 41, 2295–2300 (1990).
Fischer, M. C., GutiérrezMedina, B. & Raizen, M. G. Observation of the quantum Zeno and antiZeno effects in an unstable system. Phys. Rev. Lett. 87, 040402 (2001).
Streed, E. W. et al. Continuous and pulsed quantum Zeno effect. Phys. Rev. Lett. 97, 260402 (2006).
Kilina, S. V., Neukirch, A. J., Habenicht, B. F., Kilin, D. S. & Prezhdo, O. V. Quantum Zeno effect rationalizes the phonon bottleneck in semiconductor quantum dots. Phys. Rev. Lett. 110, 180404 (2013).
Harrington, P. M., Monroe, J. T. & Murch, K. W. Quantum Zeno effects from measurement controlled qubitbath interactions. Phys. Rev. Lett. 118, 240401 (2017).
Wang, X.B., You, J. Q. & Nori, F. Quantum entanglement via twoqubit quantum Zeno dynamics. Phys. Rev. A 77, 062339 (2008).
Maniscalco, S., Francica, F., Zaffino, R. L., Lo Gullo, N. & Plastina, F. Protecting entanglement via the quantum Zeno effect. Phys. Rev. Lett. 100, 090503 (2008).
Shao, X.Q., Chen, L., Zhang, S. & Yeon, K.H. Fast CNOT gate via quantum Zeno dynamics. J. Phys. B 42, 165507 (2009).
Chandrashekar, C. M. Zeno subspace in quantumwalk dynamics. Phys. Rev. A 82, 052108 (2010).
de Lange, G., Wang, Z. H., Ristè, D., Dobrovitski, V. V. & Hanson, R. Universal dynamical decoupling of a single solidstate spin from a spin bath. Science 330, 60–63 (2010).
Smerzi, A. Zeno dynamics, indistinguishability of state, and entanglement. Phys. Rev. Lett. 109, 150410 (2012).
PazSilva, G. A., Rezakhani, A. T., Dominy, J. M. & Lidar, D. A. Zeno effect for quantum computation and control. Phys. Rev. Lett. 108, 080501 (2012).
Zhu, B. et al. Suppressing the loss of ultracold molecules via the continuous quantum Zeno effect. Phys. Rev. Lett. 112, 070404 (2014).
Kalb, N. et al. Experimental creation of quantum Zeno subspaces by repeated multispin projections in diamond. Nat. Commun. 7, 13111 (2016).
HacohenGourgy, S., GarcíaPintos, L. P., Martin, L. S., Dressel, J. & Siddiqi, I. Incoherent qubit control using the quantum Zeno effect. Phys. Rev. Lett. 120, 020505 (2018).
Szombati, D. et al. Quantum rifling: protecting a qubit from measurement back action. Phys. Rev. Lett. 124, 070401 (2020).
Schäfer, F. et al. Experimental realization of quantum Zeno dynamics. Nat. Commun. 5, 3194 (2014).
Signoles, A. et al. Confined quantum Zeno dynamics of a watched atomic arrow. Nat. Phys. 10, 715–719 (2014).
Bretheau, L., CampagneIbarcq, P., Flurin, E., Mallet, F. & Huard, B. Quantum dynamics of an electromagnetic mode that cannot contain n photons. Science 348, 776–779 (2015).
Barontini, G., Hohmann, L., Haas, F., Estève, J. & Reichel, J. Deterministic generation of multiparticle entanglement by quantum Zeno dynamics. Science 349, 1317–1321 (2015).
Do, H. V., Gessner, M., Cataliotti, F. S. & Smerzi, A. Measuring geometric phases with a dynamical quantum Zeno effect in a BoseEinstein condensate. Phys. Rev. Res. 1, 033028 (2019).
Kofman, A. G. & Kurizki, G. Acceleration of quantum decay processes by frequent observations. Nature 405, 546 (2000).
Facchi, P. & Pascazio, S. Quantum Zeno dynamics: mathematical and physical aspects. J. Phys. A 41, 493001 (2008).
Zhou, L., Yi, W. & Cui, X. Dissipationfacilitated molecules in a fermi gas with nonhermitian spinorbit coupling. Phys. Rev. A 102, 043310 (2020).
Gou, W. et al. Tunable nonreciprocal quantum transport through a dissipative aharonovbohm ring in ultracold atoms. Phys. Rev. Lett. 124, 070402 (2020).
Bender, C. M. & Boettcher, S. Real spectra in nonhermitian hamiltonians having pt symmetry. Phys. Rev. Lett. 80, 5243–5246 (1998).
Konotop, V. V., Yang, J. & Zezyulin, D. A. Nonlinear waves in \({\mathcal{PT}}\)symmetric systems. Rev. Mod. Phys. 88, 035002 (2016).
ElGanainy, R. et al. Nonhermitian physics and \({\mathcal{PT}}\) symmetry. Nat. Phys. 14, 11 (2018).
Naghiloo, M., Abbasi, M., Joglekar, Y. N. & Murch, K. W. Quantum state tomography across the exceptional point in a single dissipative qubit. Nat. Phys. 15, 1232 (2019).
Wu, Y. et al. Observation of paritytime symmetry breaking in a singlespin system. Science 364, 878–880 (2019).
Li, J. et al. Observation of paritytime symmetry breaking transitions in a dissipative floquet system of ultracold atoms. Nat. Commun. 10, 855 (2019).
Li, J., Wang, T., Luo, L., Vemuri, S. & Joglekar, Y. N. Unification of quantum Zenoanti Zeno effects and paritytime symmetry breaking transitions. arXiv 2004.01364 (2020).
Gadway, B. Atomoptics approach to studying transport phenomena. Phys. Rev. A 92, 043606 (2015).
Meier, E. J., An, F. A. & Gadway, B. Atomoptics simulator of lattice transport phenomena. Phys. Rev. A 93, 051602 (2016).
Xie, D., Gou, W., Xiao, T., Gadway, B. & Yan, B. Topological characterizations of an extended suschriefferheeger model. npj Quantum Inf. 5, 55 (2019).
Lapp, S., Ang’ong’a, J., An, F. A. & Gadway, B. Engineering tunable local loss in a synthetic lattice of momentum states. N. J. Phys. 21, 045006 (2019).
Xie, D. et al. Topological quantum walks in momentum space with a BoseEinstein condensate. Phys. Rev. Lett. 124, 050502 (2020).
An, F. A., Meier, E. J., Ang’ong’a, J. & Gadway, B. Correlated dynamics in a synthetic lattice of momentum states. Phys. Rev. Lett. 120, 040407 (2018).
de J. LeonMontiel, R. et al. Observation of slowly decaying eigenmodes without exceptional points in floquet dissipative synthetic circuits. Commun. Phys. 1, 88 (2018).
Joglekar, Y. N. & Harter, A. K. Passive paritytimesymmetrybreaking transitions without exceptional points in dissipative photonic systems. Photon. Res. 6, A51 (2018).
Duan, L., Wang, Y.Z. & Chen, Q.H. \({\mathcal{PT}}\)symmetry of a squarewave modulated twolevel system. Chin. Phys. Lett. 37, 081101 (2020).
Harter, A. K. & Joglekar, Y. N. Connecting active and passive \({\mathcal{PT}}\)symmetric Floquet modulation models. Prog. Theor. Exp. Phys. 2020, 12A106 (2020).
Barontini, G. et al. Controlling the dynamics of an open manybody quantum system with localized dissipation. Phys. Rev. Lett. 110, 035302 (2013).
Patil, Y. S., Chakram, S. & Vengalattore, M. Measurementinduced localization of an ultracold lattice gas. Phys. Rev. Lett. 115, 140402 (2015).
Peise, J. et al. Interactionfree measurements by quantum Zeno stabilization of ultracold atoms. Nat. Commun. 6, 6811 (2015).
Everest, B., Lesanovsky, I., Garrahan, J. P. & Levi, E. Role of interactions in a dissipative manybody localized system. Phys. Rev. B 95, 024310 (2017).
RubioAbadal, A. et al. Manybody delocalization in the presence of a quantum bath. Phys. Rev. X 9, 041014 (2019).
Bouganne, R., Aguilera, M. B., Ghermaoui, A., Beugnon, J. & Gerbier, F. Anomalous decay of coherence in a dissipative manybody system. Nat. Phys. 16, 21 (2020).
Choi, J. et al. Robust dynamic hamiltonian engineering of manybody spin systems. Phys. Rev. X 10, 031002 (2020).
Acknowledgements
We acknowledge support from the National Key R&D Program of China under Grant Nos. 2018YFA0307200, 2016YFA0301700, and 2017YFA0304100, the National Natural Science Foundation of China under Grant Nos. 12074337, 11974311, and 91736209, the Natural Science Foundation of Zhejiang province under Grant Nos. LR21A040002 and LZ18A040001, Zhejiang Province Plan for Science and Technology No. 2020C01019, and the Fundamental Research Funds for the Central Universities.
Author information
Authors and Affiliations
Contributions
The experimental work and data analysis were carried out by T.C., W.G., D.X., T.X., and B.Y. Theoretical modeling and calculations were done by T.C., W.Y., and J.J. All authors discussed the results and contributed to the preparation of the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Chen, T., Gou, W., Xie, D. et al. Quantum Zeno effects across a paritytime symmetry breaking transition in atomic momentum space. npj Quantum Inf 7, 78 (2021). https://doi.org/10.1038/s4153402100417y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s4153402100417y
This article is cited by

Quantum Zeno repeaters
Scientific Reports (2022)

Engineered dissipation for quantum information science
Nature Reviews Physics (2022)

Investigation of the effect of quantum measurement on paritytime symmetry
Science China Physics, Mechanics & Astronomy (2022)