Abstract

Photon fluids have recently found applications in the simulation of a variety of physical phenomena such as superfluidity, vortex instabilities, and artificial gauge theories. Here we experimentally demonstrate the use of a photon fluid for analog gravity, i.e., the study of the physics of curved spacetime in the laboratory. While most analog gravity experiments are performed in 1+1 dimensions (one spatial plus time) and thus can only mimic 1+1D spacetime, we present a (room-temperature) photon superfluid where the geometry of a rotating acoustic black hole can be realized in 2+1D dimensions by an optical vortex. By measuring the local flow velocity and speed of waves in the photon superfluid, we identify a 2D region surrounded by an ergosphere and a spatially separated horizon.

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References

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2017 (2)

D. Dung, C. Kurtscheid, T. Damm, J. Schmitt, F. Vewinger, M. Weitz, and J. Klaers, “Variable potentials for thermalized light and coupled condensates,” Nat. Photonics 11, 565–569 (2017).
[Crossref]

T. Torres, S. Patrick, A. Coutant, M. Richartz, E. W. Tedford, and S. Weinfurtner, “Rotational superradiant scattering in a vortex flow,” Nat. Phys. 13, 833–836 (2017).
[Crossref]

2016 (2)

D. Vocke, K. Wilson, F. Marino, I. Carusotto, E. M. Wright, T. Roger, B. P. Anderson, P. Öhberg, and D. Faccio, “Role of geometry in the superfluid flow of nonlocal photon fluids,” Phys. Rev. A 94, 013849 (2016).
[Crossref]

N. Westerberg, C. Maitland, D. Faccio, K. Wilson, P. Ohberg, and E. M. Wright, “Synthetic magnetism for photon fluids,” Phys. Rev. A 94, 023805 (2016).
[Crossref]

2015 (3)

H. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaître, I. Sagnes, J. Bloch, and A. Amo, “Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” Phys. Rev. Lett. 114, 036402 (2015).
[Crossref]

M. Richartz, A. Prain, S. Liberati, and S. Weinfurtner, “Rotating black holes in a draining bathtub: superradiant scattering of gravity waves,” Phys. Rev. D 91, 124018 (2015).
[Crossref]

D. Vocke, T. Roger, F. Marino, E. M. Wright, I. Carusotto, M. Clerici, and D. Faccio, “Experimental characterization of nonlocal photon fluids,” Optica 2, 484–490 (2015).
[Crossref]

2014 (3)

A. Coutant and R. Parentani, “Hawking radiation with dispersion: the broadened horizon paradigm,” Phys. Rev. D 90, 121501 (2014).
[Crossref]

J. Steinhauer, “Observation of self-amplifying Hawking radiation in an analogue black-hole laser,” Nat. Phys. 10, 864–869 (2014).
[Crossref]

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

2013 (2)

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

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

2012 (2)

V. Fleurov and R. Schilling, “Regularization of fluctuations near the sonic horizon due to the quantum potential and its influence on Hawking radiation,” Phys. Rev. A 85, 045602 (2012).
[Crossref]

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

2011 (3)

D. D. Solnyshkov, H. Flayac, and G. Malpuech, “Black holes and wormholes in spinor polariton condensates,” Phys. Rev. B 84, 233405 (2011).
[Crossref]

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

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

2010 (4)

J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, “Bose-Einstein condensation of photons in an optical microcavity,” Nature 468, 545–548 (2010).
[Crossref]

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

O. Lahav, A. Itah, A. Blumkin, C. Gordon, S. Rinott, A. Zayats, and J. Steinhauer, “Realization of a sonic black hole analog in a Bose-Einstein condensate,” Phys. Rev. Lett. 105, 240401 (2010).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

2009 (3)

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[Crossref]

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

J. Macher and R. Parentani, “Black/white hole radiation from dispersive theories,” Phys. Rev. D 79, 124008 (2009).
[Crossref]

2008 (2)

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319, 1367–1370 (2008).
[Crossref]

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

2007 (2)

2005 (1)

C. Barcelo, S. Liberati, and M. Visser, “Analogue gravity,” Living Rev. Relativity 8, 12 (2005).
[Crossref]

2002 (1)

R. Penrose, “Gravitational collapse: the role of general relativity,” Gen. Relativity Gravitation 34, 1141–1165 (2002).
[Crossref]

1999 (2)

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[Crossref]

R. Y. Chiao and 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]

1998 (2)

T. A. Jacobson and G. E. Volovik, “Event horizons and ergoregions in 3He,” Phys. Rev. D 58, 064021 (1998).
[Crossref]

M. Visser, “Acoustic black holes: horizons, ergospheres and Hawking radiation,” Classical Quantum Gravity 15, 1767–1791 (1998).
[Crossref]

1996 (1)

M. Vaupel, K. Staliunas, and C. O. Weiss, “Hydrodynamic phenomena in laser physics: modes with flow and vortices behind an obstacle in an optical channel,” Phys. Rev. A 54, 880–892 (1996).
[Crossref]

1993 (1)

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

1992 (1)

T. Frisch, Y. Pomeau, and S. Rica, “Transition to dissipation in a model of superflow,” Phys. Rev. Lett. 69, 1644–1647 (1992).
[Crossref]

1981 (1)

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

1972 (1)

Y. B. Zel’Dovich, “Amplification of cylindrical electromagnetic waves reflected from a rotating body,” Sov. Phys. JTEP 35, 1085–1087 (1972).

1971 (1)

R. Penrose and R. Floyd, “Extraction of rotational energy from a black hole,” Nature 229, 177–179 (1971).
[Crossref]

1969 (1)

R. Penrose, “Gravitational collapse: the role of general relativity,” Riv. Nuovo Cimento Soc. Ital. Fis. 1, 252–255 (1969).
[Crossref]

Amo, A.

H. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaître, I. Sagnes, J. Bloch, and A. Amo, “Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” Phys. Rev. Lett. 114, 036402 (2015).
[Crossref]

Anderson, B. P.

D. Vocke, K. Wilson, F. Marino, I. Carusotto, E. M. Wright, T. Roger, B. P. Anderson, P. Öhberg, and D. Faccio, “Role of geometry in the superfluid flow of nonlocal photon fluids,” Phys. Rev. A 94, 013849 (2016).
[Crossref]

Bar-Ad, S.

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

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

Barcelo, C.

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

C. Barcelo, S. Liberati, and M. Visser, “Analogue gravity,” Living Rev. Relativity 8, 12 (2005).
[Crossref]

Belgiorno, F.

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

D. Faccio, F. Belgiorno, S. Cacciatori, V. Gorini, S. Liberati, and U. Moschella, Analogue Gravity Phenomenology: Analogue Spacetimes and Horizons, From Theory to Experiment (Springer, 2013), Vol. 870.

Bloch, J.

H. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaître, I. Sagnes, J. Bloch, and A. Amo, “Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” Phys. Rev. Lett. 114, 036402 (2015).
[Crossref]

Blumkin, A.

O. Lahav, A. Itah, A. Blumkin, C. Gordon, S. Rinott, A. Zayats, and J. Steinhauer, “Realization of a sonic black hole analog in a Bose-Einstein condensate,” Phys. Rev. Lett. 105, 240401 (2010).
[Crossref]

Boyce, J.

R. Y. Chiao and 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]

Braidotti, M. C.

M. C. Braidotti and C. Conti, “Quantum simulation of rainbow gravity by nonlocal nonlinearity,” arXiv:1708.02623 (2017).

Cacciatori, S.

D. Faccio, F. Belgiorno, S. Cacciatori, V. Gorini, S. Liberati, and U. Moschella, Analogue Gravity Phenomenology: Analogue Spacetimes and Horizons, From Theory to Experiment (Springer, 2013), Vol. 870.

Cacciatori, S. L.

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Carusotto, I.

D. Vocke, K. Wilson, F. Marino, I. Carusotto, E. M. Wright, T. Roger, B. P. Anderson, P. Öhberg, and D. Faccio, “Role of geometry in the superfluid flow of nonlocal photon fluids,” Phys. Rev. A 94, 013849 (2016).
[Crossref]

H. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaître, I. Sagnes, J. Bloch, and A. Amo, “Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” Phys. Rev. Lett. 114, 036402 (2015).
[Crossref]

D. Vocke, T. Roger, F. Marino, E. M. Wright, I. Carusotto, M. Clerici, and D. Faccio, “Experimental characterization of nonlocal photon fluids,” Optica 2, 484–490 (2015).
[Crossref]

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

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

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

Chiao, R. Y.

R. Y. Chiao and 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]

Ciszak, M.

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

Ciuti, C.

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

Clerici, M.

D. Vocke, T. Roger, F. Marino, E. M. Wright, I. Carusotto, M. Clerici, and D. Faccio, “Experimental characterization of nonlocal photon fluids,” Optica 2, 484–490 (2015).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Conti, C.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[Crossref]

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

M. C. Braidotti and C. Conti, “Quantum simulation of rainbow gravity by nonlocal nonlinearity,” arXiv:1708.02623 (2017).

Coutant, A.

T. Torres, S. Patrick, A. Coutant, M. Richartz, E. W. Tedford, and S. Weinfurtner, “Rotational superradiant scattering in a vortex flow,” Nat. Phys. 13, 833–836 (2017).
[Crossref]

A. Coutant and R. Parentani, “Hawking radiation with dispersion: the broadened horizon paradigm,” Phys. Rev. D 90, 121501 (2014).
[Crossref]

Dalfovo, F.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys. 71, 463–512 (1999).
[Crossref]

Damm, T.

D. Dung, C. Kurtscheid, T. Damm, J. Schmitt, F. Vewinger, M. Weitz, and J. Klaers, “Variable potentials for thermalized light and coupled condensates,” Nat. Photonics 11, 565–569 (2017).
[Crossref]

Dreischuh, A.

Dung, D.

D. Dung, C. Kurtscheid, T. Damm, J. Schmitt, F. Vewinger, M. Weitz, and J. Klaers, “Variable potentials for thermalized light and coupled condensates,” Nat. Photonics 11, 565–569 (2017).
[Crossref]

Faccio, D.

D. Vocke, K. Wilson, F. Marino, I. Carusotto, E. M. Wright, T. Roger, B. P. Anderson, P. Öhberg, and D. Faccio, “Role of geometry in the superfluid flow of nonlocal photon fluids,” Phys. Rev. A 94, 013849 (2016).
[Crossref]

N. Westerberg, C. Maitland, D. Faccio, K. Wilson, P. Ohberg, and E. M. Wright, “Synthetic magnetism for photon fluids,” Phys. Rev. A 94, 023805 (2016).
[Crossref]

D. Vocke, T. Roger, F. Marino, E. M. Wright, I. Carusotto, M. Clerici, and D. Faccio, “Experimental characterization of nonlocal photon fluids,” Optica 2, 484–490 (2015).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
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H. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaître, I. Sagnes, J. Bloch, and A. Amo, “Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons,” Phys. Rev. Lett. 114, 036402 (2015).
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D. Dung, C. Kurtscheid, T. Damm, J. Schmitt, F. Vewinger, M. Weitz, and J. Klaers, “Variable potentials for thermalized light and coupled condensates,” Nat. Photonics 11, 565–569 (2017).
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Figures (3)

Fig. 1.
Fig. 1. (a) Initial flow and sound wave velocities calculated for a photon fluid with Gaussian intensity envelope (width w 1 / e 2 = 5    mm , P = 140    mW , | γ | = 4.4 × 10 7    cm 2 / W ) and field amplitude E 0 = ρ 0 ( r ) exp ( i m θ 2 i π r / r 0 ) with r 0 = 0.5    mm and m = 2 . Total flow v tot = v r 2 + v θ 2 (red), radial flow v r (blue), and sound speed c s (black) are shown. The solid circle (square) indicates the location of the horizon (ergosphere). Inset top: 2D phase profile with values from 0 (blue) to 2 π (red). Inset bottom: near-field intensity profile (arb. units). (b) Flow and sound wave velocities after 13 cm propagation in a nonlocal nonlinear medium with the same parameters obtained from numerical integration of the NLSE [Eq. (1)].
Fig. 2.
Fig. 2. (a) Experimental setup: a continuous-wave (CW) 532 nm laser beam is launched onto a diffractive phase mask, which imprints the desired phase. Diffracted orders are selected by a spatial filter in the focus of a 4 f -imaging telescope. A mechanical shutter shuts the beam on/off, which is then launched through a 13 cm long tube filled with a nonlinear methanol graphene solution. The near-field and far-field intensities are imaged at the output facet of the sample onto a CCD camera. The spatially resolved far field is recorded by selecting small areas of the near field by an iris ( 200    μm ) that is scanned across the beam diameter. (b) Example of the spatially selected far field. The location ( K x ( x , y = 0 ) , K y ( x , y = 0 ) ) of the spot, i.e., the central peak in the far field obtained by filtering the near field with the iris for varying horizontal iris position x at a fixed vertical position y = 0 , is tracked during the scan to obtain the flow velocity. (c) and (d) Lineouts of far-field images (b) along the K y = 0 and K x = 0 axes (dotted white crosshair), respectively, as a function of iris position x .
Fig. 3.
Fig. 3. (a) Black hole with experimental parameters r 0 = 0.5    mm , m = 2 , P = 140    mW , t = 200    ms . (b) White hole with the same parameters and t = 600    ms . Experimental data shown are radial and total flow velocities (blue squares/line and red circles/line) and speed of sound (black) after propagation through 13 cm of methanol-graphene solution. Error bars are smaller than the data symbols and are therefore not shown. The horizon [ v tot ( r ) = c s ( r ) ] and ergosphere [ v r ( r ) = c s ( r ) ] are shown with blue and red dotted lines, respectively. Inset: near-field intensity distribution at the sample output. The color code shows the intensity from 0 (dark blue) to 1 W / cm 2 (dark red).

Equations (9)

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z E = i 2 k 2 E + i k n 0 Δ n E ,
Δ n = γ d r d z R ( r r , z z ) | E ( r , z ) | 2 ,
t ρ + ( ρ v ) = 0 ,
t ψ + 1 2 v 2 + c 2 γ n 0 3 ρ c 2 2 k 2 n 0 2 2 ρ ρ = 0 ,
g μ ν = ( ρ 0 c s ) 2 ( ( c s 2 v 2 ) v r r v θ v r 1 0 r v θ 0 r 2 )
κ 1 2 r ( c s 2 v r 2 ) | horizon .
ω Z v θ ( r H ) r H ,
τ 1 κ ˙ κ | κ f κ i | Δ t 1 κ .
( v x ( r ) v y ( r ) ) = c n 0 k 0 ϕ ( r ) = c n 0 k 0 ( K x ( r ) K y ( r ) ) .