Observation of anti-parity-time-symmetry, phase transitions and exceptional points in an optical fibre

The exotic physics emerging in non-Hermitian systems with balanced distributions of gain and loss has recently drawn a great deal of attention. These systems exhibit phase transitions and exceptional point singularities in their spectra, at which eigen-values and eigen-modes coalesce and the overall dimensionality is reduced. So far, these principles have been implemented at the expense of precise fabrication and tuning requirements, involving tailored nano-structured devices with controlled optical gain and loss. In this work, anti-parity-time symmetric phase transitions and exceptional point singularities are demonstrated in a single strand of single-mode telecommunication fibre, using a setup consisting of off-the-shelf components. Two propagating signals are amplified and coupled through stimulated Brillouin scattering, enabling exquisite control over the interaction-governing non-Hermitian parameters. Singular response to small-scale variations and topological features arising around the exceptional point are experimentally demonstrated with large precision, enabling robustly enhanced response to changes in Brillouin frequency shift.

1. With various non-Hermitian physics presented in the paper, the results seem well-predicted by the existing non-Hermitian physics, e.g., the eigenvalue bifurcation and encircling of the EP. While those phenomena are already demonstrated in various physical system, the potential applications of such a system is only briefly discussed in the Conclusion section. The fundamental contribution of this work is rather limited. Developing a new (fiber-based) platform for APT research is useful only in a technical way. I wonder if the significance of the work can be emphasized in terms of fundamental physics or its potential in future technology.
2. The authors claim that the work is the first realization of non-Hermitian physics in optical fiber. However, a few reports about fiber lasers based on PT symmetry have been published, for example: a. Science 03 Jan 2020, Vol. 367, Issue 6473, pp. 59-64 b. Light: Science & Applications Vol. 9, Article number: 169 (2020) c. Photonics Research Vol. 6, Issue 4, pp. A18-A22 (2018) •https://doi.org/10.1364/PRJ.6.000A18 3. An oscilloscope is used to sample the probe lights from the fiber link. More details may be provided to show how the real and the imaginary parts of the eigenvalue of the system are decoded by the Fourier transform of the sampled signal. The time domain signal along with its spectrum, which shows the detuning of eigenfrequency and variation of the power of the eigenfrequency, can be useful to visualize the behavior of the eigenvalue of the system as the parameters are adjusted. The signal processing details may be added in the Method Section or in the Supplementary Information. Reviewer #2: Remarks to the Author: The work by Bergman et. Al. describes an experimental realization of exceptional points (EP) by implementing an anti-PT symmetric Hamiltonian in a standard fiber optics. In their setup, nonlinear acousto-optical interactions provide the source of non-Hermiticity. The ability to tune the system is accomplished by controlling the pump beams. By using this platform, the authors demonstrate several EP-related features including sensitivity to perturbation and Riemann sheet topology.
While several other implementations for EPs exist, this work represents an experimental milestone because: (1) It employs standard optical components; (2) The operation point can be tuned by adjusting the pump without the need to change the system itself. This is in contrast to other platforms that require daunting fabrication efforts for each operating point. The manuscript is well-written, timely and will add an important toolbox for investigating non-Hermitian systems. I recommend it for publication after the author consider the following minor comments: in the sentence: "… a setup consisting of entirely of…". 2. The authors have demonstrated the square root sensitivity near an EP. Can they comment on whether this feature can be useful for sensing applications or not? 3. There are previous works that investigated the interplay between nonlinear interactions and EPs. It would be probably useful to cite some of this work: Optics letters 40, 5086-5089 (2015), Optics letters 40, 4575-4578, (2015), New Journal of Physics 18, 125006 (2016).

October 27, 2020
NCOMMS-20-30768A-Z: Authors Reply to Reviews We would like to thank the two reviewers and the editor for their efforts and helpful suggestions. We are glad to learn that both reviewers are supportive of the publication of our work. We addressed all comments of both reviewers in the enclosed revised manuscript, as detailed below. Changes made in the manuscript are highlighted in yellow.

Response to Reviewer #1:
Comment: "In the paper, the authors demonstrated the implementation of anti-PT symmetry between SBS probe lights in a fiber-optic system. A detailed analytical study is presented. The response of the system near the exceptional point is studied, with high resolution by adjusting the frequency detuning between the probe lights and the SBS pumps and the power of the SBS pumps, which shows a good agreement between the theoretical and experimental results. Overall, it is a well written paper that can be accepted for publication in Nature Communications, given that the following concerns are addressed satisfactorily.
Reply: We thank the reviewer for his/her support of our work.
1. With various non-Hermitian physics presented in the paper, the results seem well-predicted by the existing non-Hermitian physics, e.g., the eigenvalue bifurcation and encircling of the EP. While those phenomena are already demonstrated in various physical system, the potential applications of such a system is only briefly discussed in the conclusion section. The fundamental contribution of this work is rather limited. Developing a new (fiber-based) platform for APT research is useful only in a technical way. I wonder if the significance of the work can be emphasized in terms of fundamental physics or its potential in future technology." Reply: Our work makes several important contributions. We have demonstrated anti-PT symmetry and EP physics principles through control over frequency degrees of freedom with in-situ parametric amplification and coupling. We were able to resolve the bifurcation of eigen-values around the EP with high accuracy. In addition, the introduction of anti-PT symmetry and EP physics to standard fiber that is accessible to a wide research community, as opposed to specialty platforms, opens exciting opportunities to explore the exotic physics of non-Hermitian systems. Lastly, owing to the recent advances in Brillouin integrated photonics, the principles we demonstrated here can be carried over to integrated devices to realize configurable wavelength-selective functionalities based on broken symmetries. We address this potential in the Discussion of the revised manuscript. Reply: We thank the reviewer for addressing these important recent demonstrations of PT-symmetry in coupled fiber loops. We refer to these works in the revised manuscript. The above references share many of the characteristics of PT-symmetry and EP studies in integrated devices: the degrees of freedom are optical fields circulating in resonator paths, and precise tuning of resonance frequencies is required. By contrast, the degrees of freedom in our work are co-propagating traveling waves, and no resonances are involved, with great advantages. Our system also offers great flexibility in the tuning of the available parameters. We added a comparison, highlighting the novelty of our work, in the revised manuscript. Comment: "3. An oscilloscope is used to sample the probe lights from the fiber link. More details may be provided to show how the real and the imaginary parts of the eigenvalue of the system are decoded by the Fourier transform of the sampled signal. The time domain signal along with its spectrum, which shows the detuning of eigenfrequency and variation of the power of the eigenfrequency, can be useful to visualize the behavior of the eigenvalue of the system as the parameters are adjusted. The signal processing details may be added in the Method Section or in the Supplementary Information." Reply: Our experimental setup is mapping the complex envelopes of the two probe-wave degrees of freedom to the complex magnitudes of radio-frequency components at the coherent detector output. Therefore, the magnitudes and phases of the output probe waves are identified directly. Technically, the Fourier transform of the detected signal is calculated through sampling and off-line digital signal processing. The eigenvalues and eigenvectors of the system are not directly observed on the oscilloscope. Instead, we retrieve the 2x2 transfer matrix of the system by launching known pairs of input probe fields, and measuring the corresponding outputs. The process is repeated for a large number of pairs to improve accuracy. Once the matrix is obtained its eigenvalues are calculated offline. We added these clarifications in the revised manuscript.

Response to Reviewer #2:
Comment: "The work by Bergman et. Al. describes an experimental realization of exceptional points (EP) by implementing an anti-PT symmetric Hamiltonian in a standard fiber optics. In their setup, nonlinear acousto-optical interactions provide the source of non-Hermiticity. The ability to tune the system is accomplished by controlling the pump beams. By using this platform, the authors demonstrate several EPrelated features including sensitivity to perturbation and Riemann sheet topology.
While several other implementations for EPs exist, this work represents an experimental milestone because: (1) It employs standard optical components; (2) The operation point can be tuned by adjusting the pump without the need to change the system itself. This is in contrast to other platforms that require daunting fabrication efforts for each operating point.
The manuscript is well-written, timely and will add an important toolbox for investigating non-Hermitian systems. I recommend it for publication after the author consider the following minor comments: Reply: We thank the reviewer for his/her appreciation of our work.
1. There are a few typos across the manuscript. For instance, in the abstract there is an extra "of" in the sentence: "… a setup consisting of entirely of…"." Reply: We corrected the typos in the main text.
Comment: "2. The authors have demonstrated the square root sensitivity near an EP. Can they comment on whether this feature can be useful for sensing applications or not?" Reply: The potential for enhanced sensitivity of measurements near the EP is still being investigated by the community. Some works suggest that the larger response to small-scale variations near the EP would give rise to improved sensors. Others claim that enhanced response is accompanied by elevated noise sensitivity, which leaves the signal-to-noise ratio unchanged. We did not carry out sensing experiments as part of this work. The large tunability of our system can support further studies of this issue. We address this potential in the Discussion section of the revised manuscript.