Atom interferometers with weak-measurement path detectors and their quantum mechanical analysis
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摘要
According to the orthodox interpretation of quantum physics, wave-particle duality(WPD) is the intrinsic property of all massive microscopic particles. All gedanken or realistic experiments based on atom interferometers(AI) have so far upheld the principle of WPD, either by the mechanism of the Heisenberg's position-momentum uncertainty relation or by quantum entanglement. In this paper, we propose and make a systematic quantum mechanical analysis of several schemes of weak-measurement atom interferometer(WM-AI) and compare them with the historical schemes of strongmeasurement atom interferometer(SM-AI), such as Einstein's recoiling slit and Feynman's light microscope. As the critical part of these WM-AI setups, a weak-measurement path detector(WM-PD) deliberately interacting with the atomic internal electronic quantum states is designed and used to probe the which-path information of the atom, while only inducing negligible perturbation of the atomic center-of-mass motion. Another instrument that is used to directly interact with the atomic center-of-mass while being insensitive to the internal electronic quantum states is used to monitor the atomic centerof-mass interference pattern. Two typical schemes of WM-PD are considered. The first is the micromaser-cavity path detector, which allows us to probe the spontaneously emitted microwave photon from the incoming Rydberg atom in its excited electronic state and record unanimously the which-path information of the atom. The second is the optical-lattice Bragg-grating path detector, which can split the incoming atom beam into two different directions as determined by the internal electronic state and thus encode the which-path information of the atom into the internal states of the atom. We have used standard quantum mechanics to analyze the evolution of the atomic center-of-mass and internal electronic state wave function by directly solving Schr¨odinger's equation for the composite atom-electron-photon system in these WM-AIs. We have also compared our analysis with the theoretical and experimental studies that have been presented in the previous literature. The results show that the two sets of instruments can work separately, collectively, and without mutual exclusion to enable simultaneous observation of both wave and particle nature of the atoms to a much higher level than the historical SM-AIs, while avoiding degradation from Heisenberg's uncertainty relation and quantum entanglement. We have further investigated the space–time evolution of the internal electronic quantum state, as well as the combined atom–detector system and identified the microscopic origin and role of quantum entanglement, as emphasized in numerous previous studies. Based on these physics insights and theoretical analyses, we have proposed several new WM-AI schemes that can help to elucidate the puzzling physics of the WPD of the atoms. The principle of WM-AI scheme and quantum mechanical analyses made in this work can be directly extended to examine the principle of WPD for other massive particles.
According to the orthodox interpretation of quantum physics, wave-particle duality(WPD) is the intrinsic property of all massive microscopic particles. All gedanken or realistic experiments based on atom interferometers(AI) have so far upheld the principle of WPD, either by the mechanism of the Heisenberg's position-momentum uncertainty relation or by quantum entanglement. In this paper, we propose and make a systematic quantum mechanical analysis of several schemes of weak-measurement atom interferometer(WM-AI) and compare them with the historical schemes of strongmeasurement atom interferometer(SM-AI), such as Einstein's recoiling slit and Feynman's light microscope. As the critical part of these WM-AI setups, a weak-measurement path detector(WM-PD) deliberately interacting with the atomic internal electronic quantum states is designed and used to probe the which-path information of the atom, while only inducing negligible perturbation of the atomic center-of-mass motion. Another instrument that is used to directly interact with the atomic center-of-mass while being insensitive to the internal electronic quantum states is used to monitor the atomic centerof-mass interference pattern. Two typical schemes of WM-PD are considered. The first is the micromaser-cavity path detector, which allows us to probe the spontaneously emitted microwave photon from the incoming Rydberg atom in its excited electronic state and record unanimously the which-path information of the atom. The second is the optical-lattice Bragg-grating path detector, which can split the incoming atom beam into two different directions as determined by the internal electronic state and thus encode the which-path information of the atom into the internal states of the atom. We have used standard quantum mechanics to analyze the evolution of the atomic center-of-mass and internal electronic state wave function by directly solving Schr¨odinger's equation for the composite atom-electron-photon system in these WM-AIs. We have also compared our analysis with the theoretical and experimental studies that have been presented in the previous literature. The results show that the two sets of instruments can work separately, collectively, and without mutual exclusion to enable simultaneous observation of both wave and particle nature of the atoms to a much higher level than the historical SM-AIs, while avoiding degradation from Heisenberg's uncertainty relation and quantum entanglement. We have further investigated the space–time evolution of the internal electronic quantum state, as well as the combined atom–detector system and identified the microscopic origin and role of quantum entanglement, as emphasized in numerous previous studies. Based on these physics insights and theoretical analyses, we have proposed several new WM-AI schemes that can help to elucidate the puzzling physics of the WPD of the atoms. The principle of WM-AI scheme and quantum mechanical analyses made in this work can be directly extended to examine the principle of WPD for other massive particles.
According to the orthodox interpretation of quantum physics, wave-particle duality(WPD) is the intrinsic property of all massive microscopic particles. All gedanken or realistic experiments based on atom interferometers(AI) have so far upheld the principle of WPD, either by the mechanism of the Heisenberg's position-momentum uncertainty relation or by quantum entanglement. In this paper, we propose and make a systematic quantum mechanical analysis of several schemes of weak-measurement atom interferometer(WM-AI) and compare them with the historical schemes of strongmeasurement atom interferometer(SM-AI), such as Einstein's recoiling slit and Feynman's light microscope. As the critical part of these WM-AI setups, a weak-measurement path detector(WM-PD) deliberately interacting with the atomic internal electronic quantum states is designed and used to probe the which-path information of the atom, while only inducing negligible perturbation of the atomic center-of-mass motion. Another instrument that is used to directly interact with the atomic center-of-mass while being insensitive to the internal electronic quantum states is used to monitor the atomic centerof-mass interference pattern. Two typical schemes of WM-PD are considered. The first is the micromaser-cavity path detector, which allows us to probe the spontaneously emitted microwave photon from the incoming Rydberg atom in its excited electronic state and record unanimously the which-path information of the atom. The second is the optical-lattice Bragg-grating path detector, which can split the incoming atom beam into two different directions as determined by the internal electronic state and thus encode the which-path information of the atom into the internal states of the atom. We have used standard quantum mechanics to analyze the evolution of the atomic center-of-mass and internal electronic state wave function by directly solving Schr¨odinger's equation for the composite atom-electron-photon system in these WM-AIs. We have also compared our analysis with the theoretical and experimental studies that have been presented in the previous literature. The results show that the two sets of instruments can work separately, collectively, and without mutual exclusion to enable simultaneous observation of both wave and particle nature of the atoms to a much higher level than the historical SM-AIs, while avoiding degradation from Heisenberg's uncertainty relation and quantum entanglement. We have further investigated the space–time evolution of the internal electronic quantum state, as well as the combined atom–detector system and identified the microscopic origin and role of quantum entanglement, as emphasized in numerous previous studies. Based on these physics insights and theoretical analyses, we have proposed several new WM-AI schemes that can help to elucidate the puzzling physics of the WPD of the atoms. The principle of WM-AI scheme and quantum mechanical analyses made in this work can be directly extended to examine the principle of WPD for other massive particles.
引文
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[2] Feynman R, Leighton R and Sands M 1965 The Feynman Lectures on Physics, Vol.Ⅲ, Chap.Ⅰ(Reading:Addison Wesley)
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[12] Arndt M, Nairz O, Vos-Andreae J, Keller C, van der Zouw G and Zeilinger A 1999 Nature 401 680
[13] Andrews M R, Townsend C G, Miesner H J, Durfee D S, Kurn D M and Ketterle W 1997 Science 275 637
[14] Durr S, Nonn T and Rempe G 1998 Nature 395 33
[15] Bertet P, Osnaghi S, Rauschenbeutel A, Nogues G, Auffeves A, Brune M, Raimond J M and Haroche S 2001 Nature 411 166
[16] Zhu X, Fang X, Peng X, Feng M, Gao K and Du F 2001 J. Phys. B:At.Mol. Opt. Phys. 34 4349
[17] Hackermuller L, Uttenthaler S, Homberger K, Reiger E, Brezger B,Zeilinger A and Arndt M 2003 Phys. Rev. Lett. 91 090408
[18] Liu X J, Miao Q,Gel'mukhanov F,Patanen M, Travnikova O, Nicolas C, Agren H, Ueda K and Miron C 2015 Nat. Photon. 9 120
[19] Wang Z H, Tian Y L, Yang C, Zhang P F, Li G and Zhang T C 2016Phys. Rev. A 94 062124
[20] Scully M O, Englert B G and Walther H 1991 Nature 351 111
[21] Storey E P, Tan S, Collett M J and Walls D F 1994 Nature 367 626
[22] Englert B G, Scully M O and Walther H 1995 Nature 375 367
[23] Storey E P, Tan S M, Collett M J and Walls D F 1995 Nature 375 368
[24] Wiseman H and Harrison F 1995 Nature 377 584
[25] Jacques V, Wu E, Grosshans F, Treussart F, Grangier P, Aspect A and Roch J F 2007 Science 315 966
[26] Jacques V, Wu E, Grosshans F, Treussart F, Grangier P, Aspect A and Roch J F 2013 Phys. Rev. Lett. 110 220402
[27] Ionicioiu R and Terno D R 2011 Phys. Rev. Lett. 107 230406
[28] Tang J S, Li Y L, Xu X Y, Xiang G Y, Li C F and Guo G C 2012 Nat.Photon. 6 600
[29] Kaiser F, Coudreau T, Milman P, Ostrowsky D B and Tanzilli S 2012Science 338 637
[30] Peruzzo A,Shadbolt P,Brunner N,Popescu S and O'Brien J L 2012Science 338 634
[311] Danan A, Farfumik D, Bar-Ad S and Vaidman L 2013 Phys. Rev. Lett.111 240402
[32] Saldanha P L 2014 Phys. Rev. A 89 033825
[33] Yan H, Liao K, Deng Z, He J, Xue Z Y, Zhang Z M and Zhu S L 2015Phys. Rev. A 91 042132
[34] Li Z Y 2014 Chin. Phys. B 23 110309
[35] Li Z Y 2016 Chin. Phys. Lett. 33 080302
[36] Li Z Y 2017 Europhys. Lett. 117 50005
[37] Zhou Z Y,Zhu Z H,Liu S L,Li Y H,Shi S,Ding D S,Chen L X,Gao W, Guo G C and Shi B S 2017 Sci. Bull. 62 1185
[38] Long G, Qin W, Yang Z and Li J L 2018 Sci. Chin. Phys. Mech.&Astron. 61 030311
[39] The Nobel Prize in Physics 1989 was awarded to Norman F. Ramsey"for the invention of the separated oscillatory fields method and its use in the hydrogen maser and other atomic clocks"and Hans G. Dehmelt and Wolfgang Paul"for the development of the ion trap technique"
[40] The Nobel Prize in Physics 1997 was awarded to Steven Chu, Claude Cohen-Tannoudji,and William D Phillips"for development of methods to cool and trap atoms with laser light"
[41] The Nobel Prize in Physics 2012 was awarded to Serge Haroche and David J Wineland for"ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems"
[42] Cronin A D, Schmiedmayer J and Pritchard D E 2009 Rev. Mod. Phys.81 1051
[43] Kunze S, Durr S and Rempe G 1996 Europhys. Lett. 34 343
[44] Kunze S, Durr S,Dieckmann K,Elbs M,Ernst U,Hardell A, Wolf S and Rempe G 1997 J. Mod. Opt. 44 1863
[2] Feynman R, Leighton R and Sands M 1965 The Feynman Lectures on Physics, Vol.Ⅲ, Chap.Ⅰ(Reading:Addison Wesley)
[3] Wheeler J A 1978 Mathematical Foundations Of Quantum Theory,Marlow E R ed.(New York:Academic Press)pp. 9-48
[4] Wheeler J A 1979 Problems in the Formulations of Physics di Francia G T ed.(Amsterdam:North-Holland)
[5] Wootters W K and Zurek W H 1979 Phys. Rev. D 19 473
[6] Zurek W H 2003 Rev. Mod. Phys. 75 715
[7] Schlosshauer M 2005 Rev. Mod. Phys. 76 1267
[8] Shadbolt P, Mathews J C F, Laing A and O'Brien J L 2014 Nat. Phys.10 278
[9] Zeilinger A, Gahler R, Shull C G, Theimer W and Mampe W 1988 Rev.Mod. Phys. 60 1067
[10] Carnal O and Mlynek J 1991 Phys. Rev. Lett. 66 2689
[11] Eichman U, Bergquist J C, Bollinger J J, Gilligan J M, Itano W M,Winel and D J 1993 Phys. Rev. Lett. 70 2359
[12] Arndt M, Nairz O, Vos-Andreae J, Keller C, van der Zouw G and Zeilinger A 1999 Nature 401 680
[13] Andrews M R, Townsend C G, Miesner H J, Durfee D S, Kurn D M and Ketterle W 1997 Science 275 637
[14] Durr S, Nonn T and Rempe G 1998 Nature 395 33
[15] Bertet P, Osnaghi S, Rauschenbeutel A, Nogues G, Auffeves A, Brune M, Raimond J M and Haroche S 2001 Nature 411 166
[16] Zhu X, Fang X, Peng X, Feng M, Gao K and Du F 2001 J. Phys. B:At.Mol. Opt. Phys. 34 4349
[17] Hackermuller L, Uttenthaler S, Homberger K, Reiger E, Brezger B,Zeilinger A and Arndt M 2003 Phys. Rev. Lett. 91 090408
[18] Liu X J, Miao Q,Gel'mukhanov F,Patanen M, Travnikova O, Nicolas C, Agren H, Ueda K and Miron C 2015 Nat. Photon. 9 120
[19] Wang Z H, Tian Y L, Yang C, Zhang P F, Li G and Zhang T C 2016Phys. Rev. A 94 062124
[20] Scully M O, Englert B G and Walther H 1991 Nature 351 111
[21] Storey E P, Tan S, Collett M J and Walls D F 1994 Nature 367 626
[22] Englert B G, Scully M O and Walther H 1995 Nature 375 367
[23] Storey E P, Tan S M, Collett M J and Walls D F 1995 Nature 375 368
[24] Wiseman H and Harrison F 1995 Nature 377 584
[25] Jacques V, Wu E, Grosshans F, Treussart F, Grangier P, Aspect A and Roch J F 2007 Science 315 966
[26] Jacques V, Wu E, Grosshans F, Treussart F, Grangier P, Aspect A and Roch J F 2013 Phys. Rev. Lett. 110 220402
[27] Ionicioiu R and Terno D R 2011 Phys. Rev. Lett. 107 230406
[28] Tang J S, Li Y L, Xu X Y, Xiang G Y, Li C F and Guo G C 2012 Nat.Photon. 6 600
[29] Kaiser F, Coudreau T, Milman P, Ostrowsky D B and Tanzilli S 2012Science 338 637
[30] Peruzzo A,Shadbolt P,Brunner N,Popescu S and O'Brien J L 2012Science 338 634
[311] Danan A, Farfumik D, Bar-Ad S and Vaidman L 2013 Phys. Rev. Lett.111 240402
[32] Saldanha P L 2014 Phys. Rev. A 89 033825
[33] Yan H, Liao K, Deng Z, He J, Xue Z Y, Zhang Z M and Zhu S L 2015Phys. Rev. A 91 042132
[34] Li Z Y 2014 Chin. Phys. B 23 110309
[35] Li Z Y 2016 Chin. Phys. Lett. 33 080302
[36] Li Z Y 2017 Europhys. Lett. 117 50005
[37] Zhou Z Y,Zhu Z H,Liu S L,Li Y H,Shi S,Ding D S,Chen L X,Gao W, Guo G C and Shi B S 2017 Sci. Bull. 62 1185
[38] Long G, Qin W, Yang Z and Li J L 2018 Sci. Chin. Phys. Mech.&Astron. 61 030311
[39] The Nobel Prize in Physics 1989 was awarded to Norman F. Ramsey"for the invention of the separated oscillatory fields method and its use in the hydrogen maser and other atomic clocks"and Hans G. Dehmelt and Wolfgang Paul"for the development of the ion trap technique"
[40] The Nobel Prize in Physics 1997 was awarded to Steven Chu, Claude Cohen-Tannoudji,and William D Phillips"for development of methods to cool and trap atoms with laser light"
[41] The Nobel Prize in Physics 2012 was awarded to Serge Haroche and David J Wineland for"ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems"
[42] Cronin A D, Schmiedmayer J and Pritchard D E 2009 Rev. Mod. Phys.81 1051
[43] Kunze S, Durr S and Rempe G 1996 Europhys. Lett. 34 343
[44] Kunze S, Durr S,Dieckmann K,Elbs M,Ernst U,Hardell A, Wolf S and Rempe G 1997 J. Mod. Opt. 44 1863