Physical Review Letters

Photonic de Broglie Waves

Joseph M. Jacobson, Gunnar G. Bjork, Isaac L. Chuang, Y. Yamamoto

Published Jun 12, 1995• 296 citations

Abstract

In quantum optics an ensemble of photons is treated as a Bose condensate which has a de Broglie wavelength given by ${\ensuremath{\lambda}}_{0}/N$ where ${\ensuremath{\lambda}}_{0}$ and $N$ are the wavelength and average number of constituent photons, respectively. We describe an interferometer which is capable of measuring this de Broglie wavelength. We show specifically that a coherent state input has a de Broglie coherence length proportional to $1/\sqrt{N}$. Finally we show that the interferometer is Heisenberg limited in sensitivity ( $\ensuremath{\Delta}{\ensuremath{\varphi}}_{\mathrm{min}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/N$) and thus forms a new class of interferometers operating at the fundamental quantum limit.

DOI: 10.1103/physrevlett.74.4835

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Biphoton interference and photonic de Broglie wavelength of parametric downconverted photons

Ryōsuke Shimizu, Keiichi Edamatsu, T. Itoh

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Coherently driven photonic de Broglie Sagnac interferometer

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Phase measurement at the Heisenberg limit with three photons

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Physical Review Letters

Photonic de Broglie Waves

Joseph M. Jacobson, Gunnar G. Bjork, Isaac L. Chuang, Y. Yamamoto

Published Jun 12, 1995• 296 citations

Publisher

Abstract

In quantum optics an ensemble of photons is treated as a Bose condensate which has a de Broglie wavelength given by

{\ensuremath{\lambda}}_{0}/N

where

{\ensuremath{\lambda}}_{0}

and

N

are the wavelength and average number of constituent photons, respectively. We describe an interferometer which is capable of measuring this de Broglie wavelength. We show specifically that a coherent state input has a de Broglie coherence length proportional to

1/\sqrt{N}

. Finally we show that the interferometer is Heisenberg limited in sensitivity (

\ensuremath{\Delta}{\ensuremath{\varphi}}_{\mathrm{min}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/N

) and thus forms a new class of interferometers operating at the fundamental quantum limit.

DOI: 10.1103/physrevlett.74.4835

Related papers

Biphoton interference and photonic de Broglie wavelength of parametric downconverted photons

Ryōsuke Shimizu, Keiichi Edamatsu, T. Itoh

Summary form only given. Recently, Jacobson et al. ( see Phys. Rev. Lett., vol.74, p. 4835 (1995)) proposed the concept of "photonic de Broglie wave" in multiphoton states. They argued that the photonic de Broglie wavelength of an ensemble of photons with wavelength /spl lambda//sub 0/ and average number of photons N can be measured using a special interferometer with "effective beam splitters" that do not split the multiphoton states into constituent photons. Fonseca et al. see Phys. Rev. Lett., vol. 82, p. 2868 (1999)) measured the photonic de Broglie wavelength of a two-photon state ("biphoton") using a kind of Young's interferometer. We propose and demonstrate the measurement of photonic de Broglie wavelength of biphotons generated by parametric down-conversion utilizing the usual Mach-Zehnder interferometer.Summary form only given. Recently, Jacobson et al. ( see Phys. Rev. Lett., vol.74, p. 4835 (1995)) proposed the concept of "photonic de Broglie wave" in multiphoton states. They argued that the photonic de Broglie wavelength of an ensemble of photons with wavelength /spl lambda//sub 0/ and average number of photons N can be measured using a special interferometer with "effective beam splitters" that do not split the multiphoton states into constituent photons. Fonseca et al. see Phys. Rev. Lett., vol. 82, p. 2868 (1999)) measured the photonic de Broglie wavelength of a two-photon state ("biphoton") using a kind of Young's interferometer. We propose and demonstrate the measurement of photonic de Broglie wavelength of biphotons generated by parametric down-conversion utilizing the usual Mach-Zehnder interferometer.

Quantum Electronics and Laser Science ConferenceNov 13, 20020 citations

Deterministic control of photonic de Broglie waves using coherence optics

Byoung Seung HAM

Photonic de Broglie waves offer a unique property of quantum mechanics satisfying the complementarity between the particle and wave natures of light, where the photonic de Broglie wavelength is inversely proportional to the number of entangled photons acting on a beam splitter. Very recently, the nonclassical feature of photon bunching has been newly interpreted using the pure wave nature of coherence optics [Sci. Rep. 10, 7,309 (2020)], paving the road to unconditionally secured classical key distribution [Sci. Rep. 10, 11,687 (2020)]. Here, deterministic photonic de Broglie waves are presented in a coherence regime to uncover new insights in both fundamental quantum physics and potential applications of coherence-quantum metrology.Photonic de Broglie waves offer a unique property of quantum mechanics satisfying the complementarity between the particle and wave natures of light, where the photonic de Broglie wavelength is inversely proportional to the number of entangled photons acting on a beam splitter. Very recently, the nonclassical feature of photon bunching has been newly interpreted using the pure wave nature of coherence optics [Sci. Rep. 10, 7,309 (2020)], paving the road to unconditionally secured classical key distribution [Sci. Rep. 10, 11,687 (2020)]. Here, deterministic photonic de Broglie waves are presented in a coherence regime to uncover new insights in both fundamental quantum physics and potential applications of coherence-quantum metrology.

Scientific ReportsJul 30, 202029 citations

Coherently driven photonic de Broglie Sagnac interferometer

Byoung Seung HAM

Quantum measurements have been intensively researched over decades due to quantum advantage of Heisenberg limit beating the standard quantum limit toward potential applications of quantum metrology. The kernel of quantum measurements is in the quantum correlation between bipartite photon pairs or squeezed light quenched by one parameter over corresponding noncommuting variable satisfying Heisenberg uncertainty principle. As a result, quantum measurements bring a quantum gain of the square root law in measurement sensitivity. Photonic de Broglie waves (PBW) have been the key feature of such a gain in quantum metrology especially for phase resolution enhancement beyond the classical limit of Rayleigh criterion or simply the diffraction limit. Due to extremely low efficiency of higher-order entangled photon pair generations such as a NOON state, however, the implementation of PBW for quantum metrology has been severely limited. Here, a completely different mechanism of quantum measurements is introduced for a new type of PBW and presented for its potential application of a modified Sagnac interferometer, where the resolution enhancement is several orders of magnitude higher than its classical counterpart.Quantum measurements have been intensively researched over decades due to quantum advantage of Heisenberg limit beating the standard quantum limit toward potential applications of quantum metrology. The kernel of quantum measurements is in the quantum correlation between bipartite photon pairs or squeezed light quenched by one parameter over corresponding noncommuting variable satisfying Heisenberg uncertainty principle. As a result, quantum measurements bring a quantum gain of the square root law in measurement sensitivity. Photonic de Broglie waves (PBW) have been the key feature of such a gain in quantum metrology especially for phase resolution enhancement beyond the classical limit of Rayleigh criterion or simply the diffraction limit. Due to extremely low efficiency of higher-order entangled photon pair generations such as a NOON state, however, the implementation of PBW for quantum metrology has been severely limited. Here, a completely different mechanism of quantum measurements is introduced for a new type of PBW and presented for its potential application of a modified Sagnac interferometer, where the resolution enhancement is several orders of magnitude higher than its classical counterpart.

arXiv:2002.01753Feb 5, 20203 citations

Phase measurement at the Heisenberg limit with three photons

Haibo Wang, Takayoshi Kobayashi

We describe an interferometer which is capable of measuring phase at a Heisenberg limit of $1∕3$ . The proposed interferometer, which consumes three indistinguishable photons, consists of two beam splitters with two-third reflectivity and two mirrors. It is shown that the oscillation period of the quantum interference is three times shorter than in the classical case and the interference visibility is 100%. A de Broglie wavelength given by ${\ensuremath{\lambda}}_{0}∕3$ can then be observed in this scheme, where ${\ensuremath{\lambda}}_{0}$ is the wavelength of a single photon. Compared with similar phase measurements [Mitchell et al., Nature (London) 429, 161 (2004); Walter et al., ibid. 429, 158 (2004)] by multiphoton maximally entangled states (MES), a three-photon MES is not generated in our proposal.We describe an interferometer which is capable of measuring phase at a Heisenberg limit of $1∕3$. The proposed interferometer, which consumes three indistinguishable photons, consists of two beam splitters with two-third reflectivity and two mirrors. It is shown that the oscillation period of the quantum interference is three times shorter than in the classical case and the interference visibility is 100%. A de Broglie wavelength given by ${\ensuremath{\lambda}}_{0}∕3$ can then be observed in this scheme, where ${\ensuremath{\lambda}}_{0}$ is the wavelength of a single photon. Compared with similar phase measurements [Mitchell et al., Nature (London) 429, 161 (2004); Walter et al., ibid. 429, 158 (2004)] by multiphoton maximally entangled states (MES), a three-photon MES is not generated in our proposal.

Physical Review AFeb 15, 200541 citations

Deterministic control of photonic de Broglie waves using coherence optics: Coherence de Broglie waves

Byoung Seung HAM

In quantum mechanics, photonic de Broglie waves have been understood as a unique property of quantum mechanics satisfying the complementarity between particle and wave natures of light, where the photonic de Broglie wavelength is inversely proportional to the number of entangled photons acting on a beam splitter. Very recently, the heart of nonclassical feature of photon bunching on a beam splitter was newly interpreted using pure wave nature of coherence optics [arXiv:1911.07174v2], paving a road to unconditionally secured classical key distribution [arXiv:1807.04233v3]. Here, Mach-Zehnder interferometer-based deterministic photonic de Broglie waves are studied in a coherence regime for both fundamental physics and potential applications of coherence-quantum metrology.In quantum mechanics, photonic de Broglie waves have been understood as a unique property of quantum mechanics satisfying the complementarity between particle and wave natures of light, where the photonic de Broglie wavelength is inversely proportional to the number of entangled photons acting on a beam splitter. Very recently, the heart of nonclassical feature of photon bunching on a beam splitter was newly interpreted using pure wave nature of coherence optics [arXiv:1911.07174v2], paving a road to unconditionally secured classical key distribution [arXiv:1807.04233v3]. Here, Mach-Zehnder interferometer-based deterministic photonic de Broglie waves are studied in a coherence regime for both fundamental physics and potential applications of coherence-quantum metrology.

arXiv:2001.06913Jan 19, 20202 citations

Observing photonic de Broglie waves without the maximally-path-entangled |N,0〉+|0,N〉 state

Osung Kwon, Young-Sik Ra, Yoon-Ho Kim

The photonic de Broglie wave, in which an ensemble of $N$ identical photons with wavelength $\ensuremath{\lambda}$ reveals $\ensuremath{\lambda}/N$ interference fringes, has been known to be a unique feature exhibited by the photon-number-path--entangled $|N,0\ensuremath{\rangle}+|0,N\ensuremath{\rangle}$ state or the $N00N$ state. Here, we report the observation of the photonic de Broglie wave for a pair of photons, generated by spontaneous parametric down-conversion, that are not photon-number-path entangled. We also show that the photonic de Broglie wave can even be observed for a pair of photons that are completely separable (i.e., no entanglement in all degrees of freedom) and distinguishable. The experimental and theoretical results suggest that the photonic de Broglie wave is, in fact, not related to the entanglement of the photons, rather it is related to the indistinguishable pathways established by the measurement scheme. The phase sensitivity surpassing the standard quantum limit, however, is shown to be closely related to the $N00N$ state.The photonic de Broglie wave, in which an ensemble of $N$ identical photons with wavelength $\ensuremath{\lambda}$ reveals $\ensuremath{\lambda}/N$ interference fringes, has been known to be a unique feature exhibited by the photon-number-path--entangled $|N,0\ensuremath{\rangle}+|0,N\ensuremath{\rangle}$ state or the $N00N$ state. Here, we report the observation of the photonic de Broglie wave for a pair of photons, generated by spontaneous parametric down-conversion, that are not photon-number-path entangled. We also show that the photonic de Broglie wave can even be observed for a pair of photons that are completely separable (i.e., no entanglement in all degrees of freedom) and distinguishable. The experimental and theoretical results suggest that the photonic de Broglie wave is, in fact, not related to the entanglement of the photons, rather it is related to the indistinguishable pathways established by the measurement scheme. The phase sensitivity surpassing the standard quantum limit, however, is shown to be closely related to the $N00N$ state.

arXiv:0910.5797Physical Review AJun 1, 201041 citations

In quantum optics an ensemble of photons is treated as a Bose condensate which has a de Broglie wavelength given by

{\ensuremath{\lambda}}_{0}/N

where

{\ensuremath{\lambda}}_{0}

and

N

1/\sqrt{N}

. Finally we show that the interferometer is Heisenberg limited in sensitivity (

\ensuremath{\Delta}{\ensuremath{\varphi}}_{\mathrm{min}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/N

) and thus forms a new class of interferometers operating at the fundamental quantum limit.

We describe an interferometer which is capable of measuring phase at a Heisenberg limit of

1∕3

. The proposed interferometer, which consumes three indistinguishable photons, consists of two beam splitters with two-third reflectivity and two mirrors. It is shown that the oscillation period of the quantum interference is three times shorter than in the classical case and the interference visibility is 100%. A de Broglie wavelength given by ${\ensuremath{\lambda}}_{0}∕3$ can then be observed in this scheme, where ${\ensuremath{\lambda}}_{0}$ is the wavelength of a single photon. Compared with similar phase measurements [Mitchell et al., Nature (London) 429, 161 (2004); Walter et al., ibid. 429, 158 (2004)] by multiphoton maximally entangled states (MES), a three-photon MES is not generated in our proposal.

The photonic de Broglie wave, in which an ensemble of

N

identical photons with wavelength $\ensuremath{\lambda}$ reveals $\ensuremath{\lambda}/N$ interference fringes, has been known to be a unique feature exhibited by the photon-number-path--entangled $|N,0\ensuremath{\rangle}+|0,N\ensuremath{\rangle}$ state or the

N00N

state. Here, we report the observation of the photonic de Broglie wave for a pair of photons, generated by spontaneous parametric down-conversion, that are not photon-number-path entangled. We also show that the photonic de Broglie wave can even be observed for a pair of photons that are completely separable (i.e., no entanglement in all degrees of freedom) and distinguishable. The experimental and theoretical results suggest that the photonic de Broglie wave is, in fact, not related to the entanglement of the photons, rather it is related to the indistinguishable pathways established by the measurement scheme. The phase sensitivity surpassing the standard quantum limit, however, is shown to be closely related to the

N00N

state.