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arXiv:1703.01556

Experimental simulation of quantum temporal steering beyond rotating-wave approximation

Shao-Jie Xiong, Yu Zhang, Zhe Sun, Li Zhi Yu, Jinshuang Jin, Xiaoqiang Xu, Jin‐Ming Liu, Kefei Chen, Chui‐Ping Yang

Published Mar 5, 2017• 1 citation
arXivHTMLPDF

Abstract

Characterizing the dynamics of open systems usually starts with a perturbative theory and involves various approximations, such as the Born, Markov and rotating-wave approximation (RWA). However, the approximation approaches could introduce more or less incompleteness in describing the bath behaviors. Here, we consider a quantum channel, which is modeled by a qubit (a two-level system) interacting with a bosonic bath. Unlike the traditional works, we experimentally simulate the system-bath interaction without applying the Born, Markov, and rotating-wave approximations. To our knowledge, this is the first experimental simulation of the quantum channels without any approximations mentioned above, by using linear optical devices. The results are quite useful and interesting, which not only reveal the effect of the counter-rotating terms but also present a more accurate picture of the quantum channel dynamics. Besides, we experimentally investigate the dynamics of the quantum temporal steering (TS), i.e., a temporal analogue of Einstein-Podolsky-Rosen steering. The experimental and theoretical results are in good agreement and show that the counter-rotating terms significantly influence the TS dynamics. When one monogamously associates TS with the security of the cryptographic protocols (e.g., BB84), our experimental tests reveal that the channels based on RWA will provide exaggerated security durations, while they are actually insecure in non-RWA channel cases. This implies that doing RWA may result in a risk for the security of quantum key distribution. Our findings are expected to have useful applications in secure quantum communications and future interesting TS studies.

DOI
10.48550/arxiv.1703.01556

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Characterizing the dynamics of open systems usually starts with a perturbative theory and involves various approximations, such as the Born, Markov and rotating-wave approximation (RWA). However, the approximation approaches could introduce more or less incompleteness in describing the bath behaviors. Here, we consider a quantum channel, which is modeled by a qubit (a two-level system) interacting with a bosonic bath. Unlike the traditional works, we experimentally simulate the system-bath interaction without applying the Born, Markov, and rotating-wave approximations. To our knowledge, this is the first experimental simulation of the quantum channels without any approximations mentioned above, by using linear optical devices. The results are quite useful and interesting, which not only reveal the effect of the counter-rotating terms but also present a more accurate picture of the quantum channel dynamics. Besides, we experimentally investigate the dynamics of the quantum temporal steering (TS), i.e., a temporal analogue of Einstein-Podolsky-Rosen steering. The experimental and theoretical results are in good agreement and show that the counter-rotating terms significantly influence the TS dynamics. When one monogamously associates TS with the security of the cryptographic protocols (e.g., BB84), our experimental tests reveal that the channels based on RWA will provide exaggerated security durations, while they are actually insecure in non-RWA channel cases. This implies that doing RWA may result in a risk for the security of quantum key distribution. Our findings are expected to have useful applications in secure quantum communications and future interesting TS studies.
We experimentally simulate a quantum channel in a linear optical setup, which is modeled by a two-level system (i.e., qubit) interacting with a bosonic bath. Unlike the traditional works, we treat the system–bath interaction without applying the Born approximation, the Markov approximation, or the rotating-wave approximation (RWA). To the best of our knowledge, this is the first experimental simulation of a quantum channel without any of the approximations mentioned above by using linear optical devices. This non-RWA channel provides a more accurate picture of the quantum open-system dynamics. It not only reveals the effect of the counterrotating terms but also enables us to consider arbitrarily strong coupling regimes. With the proposed channel, we further experimentally investigate the dynamics of the quantum temporal steering (TS), i.e., a temporal analog of Einstein–Podolsky–Rosen steering. The experimental and theoretical results are in good agreement and show that the counterrotating terms significantly influence the TS dynamics. The TS in non-RWA and RWA channels presents different dynamics. However, we emphasize that the results without RWA are closer to realistic situations and thus more reliable. Due to the close relationship between TS and the security of the quantum cryptographic protocols, our findings are expected to have useful applications in secure quantum communications. This work also inspires future interest in studying other quantum coherence properties in the non-RWA channels.
By applying the hierarchy equation method, we computationally study the creation of quantum steering in a two-qubit system interacting with a common bosonic bath. The calculation does not adopt conventional approximate approaches, such as the Born, Markov, rotating-wave, and other perturbative approximations. Three kinds of quantum steering, i.e., Einstein-Podolsky-Rosen steering (EPRS), temporal steering (TS), and spatiotemporal steering (STS), are considered. Since the initial state of the two qubits is chosen as a product state, there does not exist EPRS at the beginning. During the evolution, we find that STS as well as EPRS are generated at the same time. An inversion relationship between STS and TS is revealed. By varying the system-bath coupling strength from weak to ultrastrong regimes, we find the nonmonotonic dependence of STS, TS, and EPRS on the coupling strength. It is interesting to study the dynamics of the three kinds of quantum steering by using an exactly numerical method, which is not considered in previous researches.
We experimentally investigate the non-Markovianity problems in a quantum channel implemented by an all-optical setup. The quantum channel simulates the dynamics of a two-level (qubit) system surrounded by bosonic modes, with the system-environment interaction treated without applying the rotating-wave approximation (RWA). Therefore, it allows us to demonstrate the important role of counterrotating-wave terms in influencing the memory effects of the environment. The experimental and theoretical results are in good agreement and show quite different behaviors of the non-Markovianity measure between RWA and non-RWA channels. One can find the nonmonotonic dependence of the non-Markovianity measure on the coupling and detuning parameters in the non-RWA case, which is attributed to the competing mechanisms caused by the counterrotating-wave terms. We emphasize that the non-RWA channel provides a more clear description of the open-system dynamics and the counterrotating-wave terms are indispensable in the study of non-Markovianity.
Temporal steering is a form of temporal correlation between the initial and final state of a quantum system. It is a temporal analogue of the famous Einstein-Podolsky-Rosen (spatial) steering. We demonstrate, by measuring the photon polarization, that temporal steering allows two parties to verify if they have been interacting with the same particle, even if they have no information about what happened with the particle in between the measurements. This is the first experimental study of temporal steering. We also performed experimental tests, based on the violation of temporal steering inequalities, of the security of two quantum key distribution protocols against individual attacks. Thus, these results can lead to applications for secure quantum communications and quantum engineering.
With increasing performance of actual qubit devices, even subtle effects in the interaction between qubits and environmental degrees of freedom become progressively relevant and experimentally visible. This applies particularly to the timescale separations that are at the basis of the most commonly used numerical simulation platform for qubit operations, namely, the conventional Lindblad master equation (LE): the Markov approximation and the rotating wave approximation (RWA). In this contribution, we shed light on the questions (i) to which extent it is possible to monitor violations of either of these timescale separations experimentally and (ii) which of them is the most severe to provide highly accurate predictions within (approximate) numerical schemes in relevant parameter ranges. For this purpose, we compare three simulation methods for the reduced density matrix with progressively growing accuracy. In particular, predictions for relaxation and decoherence of a qubit system in the presence of reservoirs with Ohmic and sub-Ohmic spectral densities are explored and, with the aid of proper protocols based on Ramsey experiments, the role of non-Markovianity and RWA are revealed. We discuss potential implications for future experiments and the design of approximate yet accurate numerical approaches.
Dark state as a consequence of interference between different quantum states has great importance in the fields of chip-scale atomic clock and quantum information. For the Λ-type three-level system, this dark state is generally regarded as being dissipation-free because it is a superposition of two lowest states without dipole transition between them. However, previous studies are based on the rotating-wave approximation (RWA) by neglecting the counter-rotating terms in the system-environment interaction. In this work, we study non-Markovian quantum dynamics of the dark state in a Λ-type three-level system coupled to two bosonic baths and reveal the effect of counter-rotating terms on the dark state. In contrast to the dark state within the RWA, leakage of the dark state occurs even at zero temperature, as a result of these counter-rotating terms. Also, we present a method to restore the quantum coherence of the dark state by applying a leakage elimination operator to the system.