Abstract

Quantum gases of atoms and exciton-polaritons are now well-established theoretical and experimental tools for fundamental studies of quantum many-body physics and suggest promising applications to quantum computing. Given their technological complexity, it is of paramount interest to devise other systems where such quantum many-body physics can be investigated at lesser technological expense. Here we examine a relatively well-known system of laser light propagating through thermo-optical defocusing media: based on a hydrodynamic description of light as a quantum fluid of interacting photons, we investigate such systems as a valid room-temperature alternative to atomic or exciton–polariton condensates for studies of many-body physics. First, we show that by using a technique traditionally used in oceanography it is possible to perform a direct measurement of the single-particle part of the dispersion relation of the elementary excitations on top of the photon fluid and to detect its global flow. Then, using a pump-and-probe setup, we investigate the dispersion of excitation modes of the fluid: for very long wavelengths, a sonic, dispersionless propagation is observed that we interpret as a signature of superfluid behavior.

© 2015 Optical Society of America

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References

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2014 (2)

A. Picozzi, J. Garnier, T. Hanssom, P. Suret, S. Randoux, G. Millot, D. N. Christodoulides, “Optical wave turbulence: towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542, 1–132 (2014).
[Crossref]

I. Carusotto, “Superfluid light in bulk nonlinear media,” Proc. R. Soc. A 470, 20140320 (2014).

2013 (2)

I. Carusotto, C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85, 299–366 (2013).
[Crossref]

S. Bar-Ad, R. Schilling, V. Fleurov, “Nonlocality and fluctuations near the optical analog of a sonic horizon,” Phys. Rev. A 87, 013802 (2013).
[Crossref]

2012 (3)

N. Ghofraniha, L. S. Amato, V. Folli, S. Trillo, E. DelRe, C. Conti, “Measurement of scaling laws for shock waves in thermal nonlocal media,” Opt. Lett. 37, 2325–2327 (2012).
[Crossref]

D. Gerace, I. Carusotto, “Analog Hawking radiation from an acoustic black hole in a flowing polariton superfluid,” Phys. Rev. B 86, 144505 (2012).

M. Elazar, V. Fleurov, S. Bar-Ad, “All-optical event horizon in an optical analog of a Laval nozzle,” Phys. Rev. A 86, 063821 (2012).
[Crossref]

2011 (2)

C. Barceló, S. Liberati, M. Visser, “Analogue gravity,” Living Rev. Relativity 14, 3–159 (2011).
[Crossref]

S. Weinfurtner, E. W. Tedford, M. C. J. Penrice, W. G. Unruh, G. A. Lawrence, “Measurement of stimulated Hawking emission in an analogue system,” Phys. Rev. Lett. 106, 021302 (2011).
[Crossref]

2010 (1)

I. Fouxon, O. V. Farberovich, S. Bar-Ad, V. Fleurov, “Dynamics of fluctuations in an optical analogue of the Laval nozzle,” Europhys. Lett. 92, 14002 (2010).
[Crossref]

2009 (3)

F. Marino, M. Ciszak, A. Ortolan, “Acoustic superradiance from optical vortices in self-defocusing cavities,” Phys. Rev. A 80, 065802 (2009).
[Crossref]

J. Macher, R. Parentani, “Black-hole radiation in Bose-Einstein condensates,” Phys. Rev. A 80, 043601 (2009).
[Crossref]

C. Barsi, W. Wan, J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3, 211–215 (2009).
[Crossref]

2008 (2)

2007 (4)

2001 (1)

W. Krolikowski, O. Bang, J. Rasmussen, J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[Crossref]

2000 (1)

S. Sinha, A. Ray, K. Dasgupta, “Solvent dependent nonlinear refraction in organic dye solution,” J. Appl. Phys. 87, 3222–3226 (2000).
[Crossref]

1999 (1)

R. Chiao, J. Boyce, “Bogoliubov dispersion relation and the possibility of superfluidity for weakly interacting photons in a two-dimensional photon fluid,” Phys. Rev. A 60, 4114–4121 (1999).
[Crossref]

1996 (1)

J. Dugan, H. Suzukawa, C. Forsyth, M. Farber, “Ocean wave dispersion surface measured with airborne IR imaging system,” IEEE Trans. Geosci. Remote Sens. 34, 1282–1284 (1996).
[Crossref]

1994 (2)

1993 (2)

Y. Pomeau, S. Rica, “Diffraction non linéaire,” C. R. Acad. Sci. Paris t.317, 1287–1292 (1993).

Y. Pomeau, S. Rica, “Model of superflow with rotons,” Phys. Rev. Lett. 71, 247–250 (1993).
[Crossref]

1984 (1)

1981 (1)

W. G. Unruh, “Experimental black-hole evaporation?” Phys. Rev. Lett. 46, 1351–1353 (1981).
[Crossref]

1969 (1)

D. Stilwell, “Directional energy spectra of the sea from photographs,” J. Geophys. Res. 74, 1974–1986 (1969).
[Crossref]

1927 (1)

E. Madelung, “Quantentheorie in hydrodynamischer Form,” Z. Phys. 40, 322–326 (1927).
[Crossref]

Amato, L. S.

Amo, A.

H. S. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaitre, I. Sagnes, J. Bloch, A. Amo, “An acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” arXiv:1410.0238 (2014).

Bang, O.

L. Rindorf, O. Bang, “Highly sensitive refractometer with a photonic-crystal-fiber long-period grating,” Opt. Lett. 33, 563–565 (2008).
[Crossref]

W. Krolikowski, O. Bang, J. Rasmussen, J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[Crossref]

Bar-Ad, S.

S. Bar-Ad, R. Schilling, V. Fleurov, “Nonlocality and fluctuations near the optical analog of a sonic horizon,” Phys. Rev. A 87, 013802 (2013).
[Crossref]

M. Elazar, V. Fleurov, S. Bar-Ad, “All-optical event horizon in an optical analog of a Laval nozzle,” Phys. Rev. A 86, 063821 (2012).
[Crossref]

I. Fouxon, O. V. Farberovich, S. Bar-Ad, V. Fleurov, “Dynamics of fluctuations in an optical analogue of the Laval nozzle,” Europhys. Lett. 92, 14002 (2010).
[Crossref]

Barceló, C.

C. Barceló, S. Liberati, M. Visser, “Analogue gravity,” Living Rev. Relativity 14, 3–159 (2011).
[Crossref]

Barsi, C.

C. Barsi, W. Wan, J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3, 211–215 (2009).
[Crossref]

C. Barsi, W. Wan, C. Sun, J. W. Fleischer, “Dispersive shock waves with nonlocal nonlinearity,” Opt. Lett. 32, 2930–2932 (2007).
[Crossref]

Bloch, J.

H. S. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaitre, I. Sagnes, J. Bloch, A. Amo, “An acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” arXiv:1410.0238 (2014).

Bosshard, C.

Boyce, J.

R. Chiao, J. Boyce, “Bogoliubov dispersion relation and the possibility of superfluidity for weakly interacting photons in a two-dimensional photon fluid,” Phys. Rev. A 60, 4114–4121 (1999).
[Crossref]

Carter, C. A.

Carusotto, I.

I. Carusotto, “Superfluid light in bulk nonlinear media,” Proc. R. Soc. A 470, 20140320 (2014).

I. Carusotto, C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85, 299–366 (2013).
[Crossref]

D. Gerace, I. Carusotto, “Analog Hawking radiation from an acoustic black hole in a flowing polariton superfluid,” Phys. Rev. B 86, 144505 (2012).

P.-É. Larré, I. Carusotto, “Propagation of a quantum fluid of light in a bulk nonlinear optical medium: general theory and response to a quantum quench,” arXiv:1412.5405 (2015).

H. S. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaitre, I. Sagnes, J. Bloch, A. Amo, “An acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” arXiv:1410.0238 (2014).

Chiao, R.

R. Chiao, J. Boyce, “Bogoliubov dispersion relation and the possibility of superfluidity for weakly interacting photons in a two-dimensional photon fluid,” Phys. Rev. A 60, 4114–4121 (1999).
[Crossref]

Christodoulides, D. N.

A. Picozzi, J. Garnier, T. Hanssom, P. Suret, S. Randoux, G. Millot, D. N. Christodoulides, “Optical wave turbulence: towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542, 1–132 (2014).
[Crossref]

Ciszak, M.

F. Marino, M. Ciszak, A. Ortolan, “Acoustic superradiance from optical vortices in self-defocusing cavities,” Phys. Rev. A 80, 065802 (2009).
[Crossref]

Ciuti, C.

I. Carusotto, C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85, 299–366 (2013).
[Crossref]

Conti, C.

Dasgupta, K.

S. Sinha, A. Ray, K. Dasgupta, “Solvent dependent nonlinear refraction in organic dye solution,” J. Appl. Phys. 87, 3222–3226 (2000).
[Crossref]

DelRe, E.

Dreischuh, A.

Dugan, J.

J. Dugan, H. Suzukawa, C. Forsyth, M. Farber, “Ocean wave dispersion surface measured with airborne IR imaging system,” IEEE Trans. Geosci. Remote Sens. 34, 1282–1284 (1996).
[Crossref]

Elazar, M.

M. Elazar, V. Fleurov, S. Bar-Ad, “All-optical event horizon in an optical analog of a Laval nozzle,” Phys. Rev. A 86, 063821 (2012).
[Crossref]

Farber, M.

J. Dugan, H. Suzukawa, C. Forsyth, M. Farber, “Ocean wave dispersion surface measured with airborne IR imaging system,” IEEE Trans. Geosci. Remote Sens. 34, 1282–1284 (1996).
[Crossref]

Farberovich, O. V.

I. Fouxon, O. V. Farberovich, S. Bar-Ad, V. Fleurov, “Dynamics of fluctuations in an optical analogue of the Laval nozzle,” Europhys. Lett. 92, 14002 (2010).
[Crossref]

Fleischer, J.

W. Wan, S. Jia, J. Fleischer, “Dispersive, superfluid-like shock waves in nonlinear optics,” Nat. Phys. 3, 46–51 (2007).
[Crossref]

Fleischer, J. W.

C. Barsi, W. Wan, J. W. Fleischer, “Imaging through nonlinear media using digital holography,” Nat. Photonics 3, 211–215 (2009).
[Crossref]

C. Barsi, W. Wan, C. Sun, J. W. Fleischer, “Dispersive shock waves with nonlocal nonlinearity,” Opt. Lett. 32, 2930–2932 (2007).
[Crossref]

Fleurov, V.

S. Bar-Ad, R. Schilling, V. Fleurov, “Nonlocality and fluctuations near the optical analog of a sonic horizon,” Phys. Rev. A 87, 013802 (2013).
[Crossref]

M. Elazar, V. Fleurov, S. Bar-Ad, “All-optical event horizon in an optical analog of a Laval nozzle,” Phys. Rev. A 86, 063821 (2012).
[Crossref]

I. Fouxon, O. V. Farberovich, S. Bar-Ad, V. Fleurov, “Dynamics of fluctuations in an optical analogue of the Laval nozzle,” Europhys. Lett. 92, 14002 (2010).
[Crossref]

Folli, V.

Forsyth, C.

J. Dugan, H. Suzukawa, C. Forsyth, M. Farber, “Ocean wave dispersion surface measured with airborne IR imaging system,” IEEE Trans. Geosci. Remote Sens. 34, 1282–1284 (1996).
[Crossref]

Fouxon, I.

I. Fouxon, O. V. Farberovich, S. Bar-Ad, V. Fleurov, “Dynamics of fluctuations in an optical analogue of the Laval nozzle,” Europhys. Lett. 92, 14002 (2010).
[Crossref]

Galopin, E.

H. S. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaitre, I. Sagnes, J. Bloch, A. Amo, “An acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” arXiv:1410.0238 (2014).

Garnier, J.

A. Picozzi, J. Garnier, T. Hanssom, P. Suret, S. Randoux, G. Millot, D. N. Christodoulides, “Optical wave turbulence: towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542, 1–132 (2014).
[Crossref]

Gerace, D.

D. Gerace, I. Carusotto, “Analog Hawking radiation from an acoustic black hole in a flowing polariton superfluid,” Phys. Rev. B 86, 144505 (2012).

H. S. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaitre, I. Sagnes, J. Bloch, A. Amo, “An acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” arXiv:1410.0238 (2014).

Ghofraniha, N.

Hanssom, T.

A. Picozzi, J. Garnier, T. Hanssom, P. Suret, S. Randoux, G. Millot, D. N. Christodoulides, “Optical wave turbulence: towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542, 1–132 (2014).
[Crossref]

Harris, J. M.

Jia, S.

W. Wan, S. Jia, J. Fleischer, “Dispersive, superfluid-like shock waves in nonlinear optics,” Nat. Phys. 3, 46–51 (2007).
[Crossref]

Kivshar, Y. S.

Krolikowski, W.

A. Minovich, D. N. Neshev, A. Dreischuh, W. Krolikowski, Y. S. Kivshar, “Experimental reconstruction of nonlocal response of thermal nonlinear optical media,” Opt. Lett. 32, 1599–1601 (2007).
[Crossref]

W. Krolikowski, O. Bang, J. Rasmussen, J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[Crossref]

Larré, P.-É.

P.-É. Larré, I. Carusotto, “Propagation of a quantum fluid of light in a bulk nonlinear optical medium: general theory and response to a quantum quench,” arXiv:1412.5405 (2015).

Lawrence, G. A.

S. Weinfurtner, E. W. Tedford, M. C. J. Penrice, W. G. Unruh, G. A. Lawrence, “Measurement of stimulated Hawking emission in an analogue system,” Phys. Rev. Lett. 106, 021302 (2011).
[Crossref]

Lemaitre, A.

H. S. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaitre, I. Sagnes, J. Bloch, A. Amo, “An acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” arXiv:1410.0238 (2014).

Liberati, S.

C. Barceló, S. Liberati, M. Visser, “Analogue gravity,” Living Rev. Relativity 14, 3–159 (2011).
[Crossref]

Macher, J.

J. Macher, R. Parentani, “Black-hole radiation in Bose-Einstein condensates,” Phys. Rev. A 80, 043601 (2009).
[Crossref]

Madelung, E.

E. Madelung, “Quantentheorie in hydrodynamischer Form,” Z. Phys. 40, 322–326 (1927).
[Crossref]

Mamyshev, P. V.

Marino, F.

F. Marino, M. Ciszak, A. Ortolan, “Acoustic superradiance from optical vortices in self-defocusing cavities,” Phys. Rev. A 80, 065802 (2009).
[Crossref]

F. Marino, “Acoustic black holes in a two-dimensional photon fluid,” Phys. Rev. A 78, 063804 (2008).
[Crossref]

Millot, G.

A. Picozzi, J. Garnier, T. Hanssom, P. Suret, S. Randoux, G. Millot, D. N. Christodoulides, “Optical wave turbulence: towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542, 1–132 (2014).
[Crossref]

Minovich, A.

Neshev, D. N.

Nguyen, H. S.

H. S. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaitre, I. Sagnes, J. Bloch, A. Amo, “An acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” arXiv:1410.0238 (2014).

Ortolan, A.

F. Marino, M. Ciszak, A. Ortolan, “Acoustic superradiance from optical vortices in self-defocusing cavities,” Phys. Rev. A 80, 065802 (2009).
[Crossref]

Parentani, R.

J. Macher, R. Parentani, “Black-hole radiation in Bose-Einstein condensates,” Phys. Rev. A 80, 043601 (2009).
[Crossref]

Penrice, M. C. J.

S. Weinfurtner, E. W. Tedford, M. C. J. Penrice, W. G. Unruh, G. A. Lawrence, “Measurement of stimulated Hawking emission in an analogue system,” Phys. Rev. Lett. 106, 021302 (2011).
[Crossref]

Picozzi, A.

A. Picozzi, J. Garnier, T. Hanssom, P. Suret, S. Randoux, G. Millot, D. N. Christodoulides, “Optical wave turbulence: towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542, 1–132 (2014).
[Crossref]

Pitaevskii, L. P.

L. P. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Clarendon, 2003).

Pomeau, Y.

Y. Pomeau, S. Rica, “Model of superflow with rotons,” Phys. Rev. Lett. 71, 247–250 (1993).
[Crossref]

Y. Pomeau, S. Rica, “Diffraction non linéaire,” C. R. Acad. Sci. Paris t.317, 1287–1292 (1993).

Randoux, S.

A. Picozzi, J. Garnier, T. Hanssom, P. Suret, S. Randoux, G. Millot, D. N. Christodoulides, “Optical wave turbulence: towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542, 1–132 (2014).
[Crossref]

Rasmussen, J.

W. Krolikowski, O. Bang, J. Rasmussen, J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
[Crossref]

Ray, A.

S. Sinha, A. Ray, K. Dasgupta, “Solvent dependent nonlinear refraction in organic dye solution,” J. Appl. Phys. 87, 3222–3226 (2000).
[Crossref]

Rica, S.

Y. Pomeau, S. Rica, “Model of superflow with rotons,” Phys. Rev. Lett. 71, 247–250 (1993).
[Crossref]

Y. Pomeau, S. Rica, “Diffraction non linéaire,” C. R. Acad. Sci. Paris t.317, 1287–1292 (1993).

Rindorf, L.

Ruocco, G.

N. Ghofraniha, C. Conti, G. Ruocco, S. Trillo, “Shocks in nonlocal media,” Phys. Rev. Lett. 99, 043903 (2007).
[Crossref]

Sagnes, I.

H. S. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaitre, I. Sagnes, J. Bloch, A. Amo, “An acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” arXiv:1410.0238 (2014).

Sanvitto, D.

H. S. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaitre, I. Sagnes, J. Bloch, A. Amo, “An acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” arXiv:1410.0238 (2014).

Schilling, R.

S. Bar-Ad, R. Schilling, V. Fleurov, “Nonlocality and fluctuations near the optical analog of a sonic horizon,” Phys. Rev. A 87, 013802 (2013).
[Crossref]

Sinha, S.

S. Sinha, A. Ray, K. Dasgupta, “Solvent dependent nonlinear refraction in organic dye solution,” J. Appl. Phys. 87, 3222–3226 (2000).
[Crossref]

Stegeman, G. I.

Stilwell, D.

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Figures (4)

Fig. 1.
Fig. 1.

Bogoliubov dispersion relation according to Eqs. (5) and (7). Local nonlinear media ( Δ n = 10 4 ) show a linear part for wavelengths Λ ξ and | Δ n | > 0 (black solid line, ξ 23 μm , equivalent to K = 2.7 × 10 5 1 / m ). In nonlocal media, the effectiveness of the nonlinearity is suppressed for wavelengths Λ < σ L that result in a parabolic dispersion relation (the dashed blue lines correspond to a nonlocal nonlinear dispersion with σ L = 1 , 5 and 10 μm).

Fig. 2.
Fig. 2.

(a) Experimental layout used for measuring the dispersion relation. A collimated, flat beam is launched through a cylindrical sample filled with a methanol/graphene solution and is imaged by a camera/lens system that can be translated along the propagation direction of the beam. (b) Detail of nonlinear sample showing example beam profiles at different propagation distances (i.e., equivalently for different propagation times) as measured in the experiment. An interferometer placed before the sample generates a pump and probe beam with a controllable relative angle (i.e., wavelength of the photon fluid excitations).

Fig. 3.
Fig. 3.

Photon fluid dispersion relation with scanning distances of (a) 1.5 cm, (b) 5 cm, and (c) 12 cm. The flow v of the effective medium can be controlled by the phase of the background field: (a) v bg = 0 m / s , (b)  v bg = 1.3 × 10 6 m / s , and (c) v bg = 3.0 × 10 6 m / s .

Fig. 4.
Fig. 4.

(a) Raw data image of the beam at the sample output. The sound wave is barely visible due to the low (less than 10%) contrast of the amplitude modulation. (b) Amplitude profile of the sound wave after subtracting the pump beam profile for two different input pump powers: low-power measurement (dotted blue line) and high-power measurement (showing a shift in the wave, indicated by the arrow; solid red line). (c) Relative shift Δ S versus Λ : the solid green line shows the predicted shift for a local nonlinearity of Δ n = 7.6 × 10 6 ; the corresponding healing length is ζ = 85 μm . The solid blue line includes a nonlocal nonlinearity with Δ n = 7.6 × 10 6 and nonlocal length σ L = 110 μm . The shaded gray area ( Λ 10 ζ ) highlights the region in which, even in the presence of nonlocality, the medium acts as a superfluid. The black squares indicate the measured shift values at various wavelengths, several of which (i.e., for Λ > 0.7 mm ) lie in the superfluid region.

Equations (8)

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z E = i 2 k 2 E i k n 2 n 0 | E | 2 E ,
τ ρ + ( ρ v ) = 0 ,
τ ψ + 1 2 v 2 + c 2 n 2 n 0 3 ρ c 2 2 k 2 n 0 2 2 ρ ρ = 0 ,
ϵ = α K u K exp ( i Ω τ + i K r ) + α K * v K exp ( i Ω τ i K r ) ,
( Ω v K ) 2 = c 2 n 2 | E bg | 2 n 0 3 K 2 + c 2 4 k 2 n 0 2 K 4 .
Δ n ( r , z ) = γ R ( r r ) I ( r ) d r d z ,
( Ω v K ) 2 = c 2 n 2 | E bg | 2 n 0 3 R ^ ( K , n 0 Ω / c ) K 2 + c 2 4 k 2 n 0 2 K 4 ,
Δ S = K 2 k [ 1 + | Δ n | n 0 R ^ ( K ) ( 2 k K ) 2 1 ] z .

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