1ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
2Faculty of Physics, University of Warsaw, ul. Pasteura 5, PL-02-093 Warsaw, Poland
3Department of Physics, University of Tehran, P.O. Box 14395-547, Tehran, Iran
4School of Nano Science, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran
5ICREA – Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
6Institute of Physics PAS, Aleja Lotnikow 32/46, 02-668 Warszawa, Poland
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
In this work, we study temperature sensing with finite-sized strongly correlated systems exhibiting quantum phase transitions. We use the quantum Fisher information (QFI) approach to quantify the sensitivity in the temperature estimation, and apply a finite-size scaling framework to link this sensitivity to critical exponents of the system around critical points. We numerically calculate the QFI around the critical points for two experimentally-realizable systems: the spin-1 Bose-Einstein condensate and the spin-chain Heisenberg XX model in the presence of an external magnetic field. Our results confirm finite-size scaling properties of the QFI. Furthermore, we discuss experimentally-accessible observables that (nearly) saturate the QFI at the critical points for these two systems.
► BibTeX data
► References
[1] Carl W. Helstrom. “Quantum detection and estimation theory”. Journal of Statistical Physics 1, 231–252 (1969).
https://doi.org/10.1007/BF01007479
[2] E. O. Göbel and U. Siegner. “Quantum metrology: Foundation of Units and Measurements”. Wiley-VCH. (2015).
https://doi.org/10.1002/9783527680887
[3] Samuel L. Braunstein and Carlton M. Caves. “Statistical distance and the geometry of quantum states”. Physical Review Letters 72, 3439–3443 (1994).
https://doi.org/10.1103/PhysRevLett.72.3439
[4] M. M. Taddei, B. M. Escher, L. Davidovich, and R. L. de Matos Filho. “Quantum Speed Limit for Physical Processes”. Physical Review Letters 110, 050402 (2013). arXiv:1209.0362.
https://doi.org/10.1103/PhysRevLett.110.050402
arXiv:1209.0362
[5] Géza Tóth and Iagoba Apellaniz. “Quantum metrology from a quantum information science perspective”. Journal of Physics A: Mathematical and Theoretical 47, 424006 (2014). arXiv:1405.4878.
https://doi.org/10.1088/1751-8113/47/42/424006
arXiv:1405.4878
[6] Luca Pezzé and Augusto Smerzi. “Quantum theory of phase estimation” (2014). arXiv:1411.5164.
arXiv:1411.5164
[7] M. Napolitano, M. Koschorreck, B. Dubost, N. Behbood, R. J. Sewell, and M. W. Mitchell. “Interaction-based quantum metrology showing scaling beyond the Heisenberg limit”. Nature 471, 486–489 (2011). arXiv:1012.5787.
https://doi.org/10.1038/nature09778
arXiv:1012.5787
[8] Paolo Zanardi, Matteo G. A. Paris, and Lorenzo Campos Venuti. “Quantum criticality as a resource for quantum estimation”. Physical Review A 78, 042105 (2008). arXiv:0708.1089.
https://doi.org/10.1103/PhysRevA.78.042105
arXiv:0708.1089
[9] Wai-Keong Mok, Kishor Bharti, Leong-Chuan Kwek, and Abolfazl Bayat. “Optimal probes for global quantum thermometry”. Communications Physics 4, 62 (2021). arXiv:2010.14200.
https://doi.org/10.1038/s42005-021-00572-w
arXiv:2010.14200
[10] Karol Gietka, Friederike Metz, Tim Keller, and Jing Li. “Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied”. Quantum 5, 489 (2021). arXiv:2103.12939.
https://doi.org/10.22331/q-2021-07-01-489
arXiv:2103.12939
[11] Yaoming Chu, Shaoliang Zhang, Baiyi Yu, and Jianming Cai. “Dynamic Framework for Criticality-Enhanced Quantum Sensing”. Physical Review Letters 126, 010502 (2021). arXiv:2008.11381.
https://doi.org/10.1103/PhysRevLett.126.010502
arXiv:2008.11381
[12] Louis Garbe, Matteo Bina, Arne Keller, Matteo G. A. Paris, and Simone Felicetti. “Critical Quantum Metrology with a Finite-Component Quantum Phase Transition”. Physical Review Letters 124, 120504 (2020). arXiv:1910.00604.
https://doi.org/10.1103/PhysRevLett.124.120504
arXiv:1910.00604
[13] Marek M. Rams, Piotr Sierant, Omyoti Dutta, Paweł Horodecki, and Jakub Zakrzewski. “At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited”. Physical Review X 8, 021022 (2018). arXiv:1702.05660.
https://doi.org/10.1103/PhysRevX.8.021022
arXiv:1702.05660
[14] Safoura S. Mirkhalaf, Emilia Witkowska, and Luca Lepori. “Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate”. Physical Review A 101, 043609 (2020). arXiv:1912.02418.
https://doi.org/10.1103/PhysRevA.101.043609
arXiv:1912.02418
[15] Safoura S. Mirkhalaf, Daniel Benedicto Orenes, Morgan W. Mitchell, and Emilia Witkowska. “Criticality-enhanced quantum sensing in ferromagnetic bose-einstein condensates: Role of readout measurement and detection noise”. Physical Review A 103, 023317 (2021). arXiv:2010.13133.
https://doi.org/10.1103/PhysRevA.103.023317
arXiv:2010.13133
[16] Luca Pezzé, Andreas Trenkwalder, and Marco Fattori. “Adiabatic Sensing Enhanced by Quantum Criticality” (2019). arXiv:1906.01447.
arXiv:1906.01447
[17] Giulio Salvatori, Antonio Mandarino, and Matteo G. A. Paris. “Quantum metrology in Lipkin-Meshkov-Glick critical systems”. Physical Review A 90, 022111 (2014). arXiv:1406.5766.
https://doi.org/10.1103/PhysRevA.90.022111
arXiv:1406.5766
[18] Mankei Tsang. “Quantum transition-edge detectors”. Physical Review A 88, 021801 (2013). arXiv:1305.1750.
https://doi.org/10.1103/PhysRevA.88.021801
arXiv:1305.1750
[19] Paolo Zanardi, H.T. Quan, Xiaoguang Wang, and C.P. Sun. “Mixed-state fidelity and quantum criticality at finite temperature”. Physical Review A 75, 032109 (2007). arXiv:quant-ph/0612008.
https://doi.org/10.1103/PhysRevA.75.032109
arXiv:quant-ph/0612008
[20] Wen-Long You, Ying-Wai Li, and Shi-Jian Gu. “Fidelity, dynamic structure factor, and susceptibility in critical phenomena”. Physical Review E 76, 022101 (2007). arXiv:quant-ph/0701077.
https://doi.org/10.1103/PhysRevE.76.022101
arXiv:quant-ph/0701077
[21] Philipp Hauke, Markus Heyl, Luca Tagliacozzo, and Peter Zoller. “Measuring multipartite entanglement through dynamic susceptibilities”. Nature Physics 12, 778–782 (2016). arXiv:1509.01739.
https://doi.org/10.1038/nphys3700
arXiv:1509.01739
[22] Shi-Jian Gu. “Fidelity approach to quantum phase transitions”. International Journal of Modern Physics B 24, 4371–4458 (2010). arXiv:0811.3127.
https://doi.org/10.1142/s0217979210056335
arXiv:0811.3127
[23] Yuto Ashida, Keiji Saito, and Masahito Ueda. “Thermalization and Heating Dynamics in Open Generic Many-Body Systems”. Physical Review Letters 121 (2018). arXiv:1807.00019.
https://doi.org/10.1103/physrevlett.121.170402
arXiv:1807.00019
[24] Peter A. Ivanov. “Quantum thermometry with trapped ions”. Optics Communications 436, 101–107 (2019). arXiv:1809.01451.
https://doi.org/10.1016/j.optcom.2018.12.013
arXiv:1809.01451
[25] Michael Vennettilli, Soutick Saha, Ushasi Roy, and Andrew Mugler. “Precision of protein thermometry”. Physical Review Letters 127, 098102 (2021). arXiv:2012.02918.
https://doi.org/10.1103/PhysRevLett.127.098102
arXiv:2012.02918
[26] M. A. Continentino. “Quantum scaling in many-body systems”. World Scientific Publishing, Singapore. (2001).
https://doi.org/10.1017/CBO9781316576854
[27] J. Cardy, editor. “Finite-size scaling”. Elsevier Science Publisher, Amsterdam: North Holland. (1988). url: www.elsevier.com/books/finite-size-scaling/cardy/978-0-444-87109-1.
https://www.elsevier.com/books/finite-size-scaling/cardy/978-0-444-87109-1
[28] Massimo Campostrini, Andrea Pelissetto, and Ettore Vicari. “Finite-size scaling at quantum transitions”. Physical Review B 89 (2014). arXiv:1401.0788.
https://doi.org/10.1103/physrevb.89.094516
arXiv:1401.0788
[29] Paolo Zanardi, Paolo Giorda, and Marco Cozzini. “Information-Theoretic Differential Geometry of Quantum Phase Transitions”. Physical Review Letters 99, 100603 (2007).
https://doi.org/10.1103/PhysRevLett.99.100603
[30] Paolo Zanardi, Lorenzo Campos Venuti, and Paolo Giorda. “Bures metric over thermal state manifolds and quantum criticality”. Physical Review A 76, 062318 (2007). arXiv:0707.2772.
https://doi.org/10.1103/PhysRevA.76.062318
arXiv:0707.2772
[31] Yi-Quan Zou, Ling-Na Wu, Qi Liu, Xin-Yu Luo, Shuai-Feng Guo, Jia-Hao Cao, Meng Khoon Tey, and Li You. “Beating the classical precision limit with spin-1 dicke states of more than 10,000 atoms”. Proceedings of the National Academy of Sciences 115, 6381–6385 (2018). arXiv:1802.10288.
https://doi.org/10.1073/pnas.1715105115
arXiv:1802.10288
[32] Paul Niklas Jepsen, Jesse Amato-Grill, Ivana Dimitrova, Wen Wei Ho, Eugene Demler, and Wolfgang Ketterle. “Spin transport in a tunable heisenberg model realized with ultracold atoms”. Nature 588, 403–407 (2020). arXiv:2005.09549.
https://doi.org/10.1038/s41586-020-3033-y
arXiv:2005.09549
[33] Michael Hohmann, Farina Kindermann, Tobias Lausch, Daniel Mayer, Felix Schmidt, and Artur Widera. “Single-atom thermometer for ultracold gases”. Physical Review A 93, 043607 (2016). arXiv:1601.06067.
https://doi.org/10.1103/PhysRevA.93.043607
arXiv:1601.06067
[34] Quentin Bouton, Jens Nettersheim, Daniel Adam, Felix Schmidt, Daniel Mayer, Tobias Lausch, Eberhard Tiemann, and Artur Widera. “Single-atom quantum probes for ultracold gases boosted by nonequilibrium spin dynamics”. Physical Review X 10, 011018 (2020).
https://doi.org/10.1103/PhysRevX.10.011018
[35] A.E. Leanhardt, T.A. Pasquini, M. Saba, A. Schirotzek, Y. Shin, D. Kielpinski, D.E. Pritchard, and W. Ketterle. “Cooling Bose-Einstein condensates below 500 picokelvin”. Science 301, 1513–1515 (2003).
https://doi.org/10.1126/science.1088827
[36] Ryan Olf, Fang Fang, G. Edward Marti, Andrew MacRae, and Dan M Stamper-Kurn. “Thermometry and cooling of a Bose gas to 0.02 times the condensation temperature”. Nature Physics 11, 720–723 (2015). arXiv:1505.06196.
https://doi.org/10.1038/nphys3408
arXiv:1505.06196
[37] Matteo G.A. Paris. “Achieving the Landau bound to precision of quantum thermometry in systems with vanishing gap”. Journal of Physics A: Mathematical and Theoretical 49, 03LT02 (2015). arXiv:1510.08111.
https://doi.org/10.1088/1751-8113/49/3/03lt02
arXiv:1510.08111
[38] Mohammad Mehboudi, Anna Sanpera, and Luis A Correa. “Thermometry in the quantum regime: recent theoretical progress”. Journal of Physics A: Mathematical and Theoretical 52, 303001 (2019). arXiv:1811.03988.
https://doi.org/10.1088/1751-8121/ab2828
arXiv:1811.03988
[39] Harald Cramér. “Mathematical Methods of Statistics”. Princeton University Press. (1999). url: www.jstor.org/stable/j.ctt1bpm9r4.
https://www.jstor.org/stable/j.ctt1bpm9r4
[40] S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar. “Continuous quantum phase transitions”. Reviews of Modern Physics 69 (1997).
https://doi.org/10.1103/revmodphys.69.315
[41] Andrea Pelissetto and Ettore Vicari. “Critical phenomena and renormalization-group theory”. Physics Reports 368, 549–727 (2002). arXiv:cond-mat/0012164.
https://doi.org/10.1016/s0370-1573(02)00219-3
arXiv:cond-mat/0012164
[42] Michael E. Fisher and Michael N. Barber. “Scaling Theory for Finite-Size Effects in the Critical Region”. Physical Review Letters 28, 1516–1519 (1972).
https://doi.org/10.1103/PhysRevLett.28.1516
[43] R. Botet and R. Jullien. “Large-size critical behavior of infinitely coordinated systems”. Physical Review B 28, 3955–3967 (1983).
https://doi.org/10.1103/PhysRevB.28.3955
[44] Davide Rossini and Ettore Vicari. “Ground-state fidelity at first-order quantum transitions”. Physical Review E 98 (2018). arXiv:1807.01674.
https://doi.org/10.1103/PhysRevE.98.062137
arXiv:1807.01674
[45] Mateusz Łącki and Bogdan Damski. “Spatial Kibble–Zurek mechanism through susceptibilities: the inhomogeneous quantum Ising model case”. Journal of Statistical Mechanics: Theory and Experiment 2017, 103105 (2017). arXiv:1707.09884.
https://doi.org/10.1088/1742-5468/aa8c20
arXiv:1707.09884
[46] Luis A. Correa, Mohammad Mehboudi, Gerardo Adesso, and Anna Sanpera. “Individual Quantum Probes for Optimal Thermometry”. Physical Review Letters 114, 220405 (2015). arXiv:1411.2437.
https://doi.org/10.1103/PhysRevLett.114.220405
arXiv:1411.2437
[47] H.J. Lipkin, N. Meshkov, and A.J. Glick. “Validity of many-body approximation methods for a solvable model: (i). Exact solutions and perturbation theory”. Nuclear Physics 62, 188–198 (1965).
https://doi.org/10.1016/0029-5582(65)90862-X
[48] Yuki Kawaguchi and Masahito Ueda. “Spinor Bose–Einstein condensates”. Physics Reports 520, 253 – 381 (2012). arXiv:1001.2072.
https://doi.org/10.1016/j.physrep.2012.07.005
arXiv:1001.2072
[49] Dan M. Stamper-Kurn and Masahito Ueda. “Spinor Bose gases: Symmetries, magnetism, and quantum dynamics”. Rev. Mod. Phys. 85, 1191–1244 (2013). arXiv:1205.1888.
https://doi.org/10.1103/RevModPhys.85.1191
arXiv:1205.1888
[50] Daniel Benedicto Orenes, Anna U Kowalczyk, Emilia Witkowska, and Giovanni Barontini. “Exploring the thermodynamics of spin-1 bose gases with synthetic magnetization”. New Journal of Physics 21, 043024 (2019). arXiv:1901.00427.
https://doi.org/10.1088/1367-2630/ab14b4
arXiv:1901.00427
[51] Ming Xue, Shuai Yin, and Li You. “Universal driven critical dynamics across a quantum phase transition in ferromagnetic spinor atomic Bose-Einstein condensates”. Physical Review A 98, 013619 (2018). arXiv:1805.02174.
https://doi.org/10.1103/PhysRevA.98.013619
arXiv:1805.02174
[52] Sébastien Dusuel and Julien Vidal. “Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick model”. Physical Review Letters 93, 237204 (2004).
https://doi.org/10.1103/PhysRevLett.93.237204
[53] Bertrand Evrard, An Qu, Jean Dalibard, and Fabrice Gerbier. “Production and characterization of a fragmented spinor Bose-Einstein condensate” (2020). arXiv:2010.15739.
arXiv:2010.15739
[54] A. Langari. “Quantum renormalization group of XYZ model in a transverse magnetic field”. Physical Review B 69 (2004).
https://doi.org/10.1103/physrevb.69.100402
[55] Fabio Franchini. “An Introduction to Integrable Techniques for One-Dimensional Quantum Systems”. Springer International Publishing. (2017). arXiv:1609.02100.
https://doi.org/10.1007/978-3-319-48487-7
arXiv:1609.02100
[56] Ian Affleck and Masaki Oshikawa. “Field-induced gap in Cu benzoate and other $s=frac{1}{2}$ antiferromagnetic chains”. Physical Review B 60, 1038–1056 (1999). arXiv:cond-mat/9905002.
https://doi.org/10.1103/PhysRevB.60.1038
arXiv:cond-mat/9905002
[57] Hans-Jürgen Mikeska and Alexei K. Kolezhuk. “One-dimensional magnetism”. Chapter 1, pages 1–83. Springer Berlin Heidelberg. Berlin, Heidelberg (2004).
https://doi.org/10.1007/BFb0119591
[58] Mohammad Mehboudi, Maria Moreno-Cardoner, Gabriele De Chiara, and Anna Sanpera. “Thermometry precision in strongly correlated ultracold lattice gases”. New Journal of Physics 17, 055020 (2015). arXiv:1501.03095.
https://doi.org/10.1088/1367-2630/17/5/055020
arXiv:1501.03095
[59] Michael Hartmann, Günter Mahler, and Ortwin Hess. “Local versus global thermal states: Correlations and the existence of local temperatures”. Phys. Rev. E 70, 066148 (2004). arXiv:quant-ph/0404164.
https://doi.org/10.1103/PhysRevE.70.066148
arXiv:quant-ph/0404164
[60] Michael Hartmann, Günter Mahler, and Ortwin Hess. “Existence of Temperature on the Nanoscale”. Phys. Rev. Lett. 93, 080402 (2004). arXiv:quant-ph/0312214.
https://doi.org/10.1103/PhysRevLett.93.080402
arXiv:quant-ph/0312214
[61] Artur García-Saez, Alessandro Ferraro, and Antonio Acín. “Local temperature in quantum thermal states”. Phys. Rev. A 79, 052340 (2009). arXiv:0808.0102.
https://doi.org/10.1103/PhysRevA.79.052340
arXiv:0808.0102
[62] Alessandro Ferraro, Artur García-Saez, and Antonio Acín. “Intensive temperature and quantum correlations for refined quantum measurements”. EPL (Europhysics Letters) 98, 10009 (2012). arXiv:1102.5710.
https://doi.org/10.1209/0295-5075/98/10009
arXiv:1102.5710
[63] M. Kliesch, C. Gogolin, M. J. Kastoryano, A. Riera, and J. Eisert. “Locality of Temperature”. Phys. Rev. X 4, 031019 (2014). arXiv:1309.0816.
https://doi.org/10.1103/PhysRevX.4.031019
arXiv:1309.0816
[64] Senaida Hernández-Santana, Arnau Riera, Karen V. Hovhannisyan, Martí Perarnau-Llobet, Luca Tagliacozzo, and Antonio Acín. “Locality of temperature in spin chains”. New Journal of Physics 17, 085007 (2015). arXiv:1506.04060.
https://doi.org/10.1088/1367-2630/17/8/085007
arXiv:1506.04060
[65] Senaida Hernández-Santana, András Molnár, Christian Gogolin, J. Ignacio Cirac, and Antonio Acín. “Locality of temperature and correlations in the presence of non-zero-temperature phase transitions”. New Journal of Physics 23, 073052 (2021). arXiv:2010.15256.
https://doi.org/10.1088/1367-2630/ac14a9
arXiv:2010.15256
[66] Silvana Palacios, Simon Coop, Pau Gomez, Thomas Vanderbruggen, Y. Natali Martinez de Escobar, Martijn Jasperse, and Morgan W. Mitchell. “Multi-second magnetic coherence in a single domain spinor Bose–Einstein condensate”. New Journal of Physics 20, 053008 (2018). arXiv:1707.09607.
https://doi.org/10.1088/1367-2630/aab2a0
arXiv:1707.09607
[67] Pau Gomez, Ferran Martin, Chiara Mazzinghi, Daniel Benedicto Orenes, Silvana Palacios, and Morgan W. Mitchell. “Bose-Einstein Condensate Comagnetometer”. Physical Review Letters 124, 170401 (2020). arXiv:1910.06642.
https://doi.org/10.1103/PhysRevLett.124.170401
arXiv:1910.06642
[68] Kai Eckert, Oriol Romero-Isart, Mirta Rodriguez, Maciej Lewenstein, Eugene S Polzik, and Anna Sanpera. “Quantum non-demolition detection of strongly correlated systems”. Nature Physics 4, 50–54 (2008). arXiv:0709.0527.
https://doi.org/10.1038/nphys776
arXiv:0709.0527
[69] Yink Loong Len, Tuvia Gefen, Alex Retzker, and Jan Kołodyński. “Quantum metrology with imperfect measurements” (2021). arXiv:2109.01160.
arXiv:2109.01160
[70] Marcin Płodzień, Rafał Demkowicz-Dobrzańki, and Tomasz Sowiński. “Few-fermion thermometry”. Physical Review A 97, 063619 (2018). arXiv:1804.04506.
https://doi.org/10.1103/PhysRevA.97.063619
arXiv:1804.04506
Cited by
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.