Imaging Spatiotemporal Hong-Ou-Mandel Interference of Biphoton States of Extremely High Schmidt Number

Abstract

We report the experimental observation of a spatiotemporal Hong-Ou-Mandel (HOM) interference of biphoton states of extremely high Schmidt number. Two-photon interference of 1500 spatial modes and a total of more than 3 × 10 6 spatiotemporal modes is evidenced by measuring momentum spatial coincidences, without any prior selection of the photons in time and space coincidence, between the pixels of the far-field images of two strongly multimode spontaneous parametric down-conversion (SPDC) beams propagating through a HOM interferometer. The outgoing SPDC beams are recorded on two separate detector arrays operating in the photon-counting regime. The properties of HOM interference are investigated both in the time and space domains. We show that the two-photon interference exhibits temporal and two-dimensional spatial HOM dips with visibilities of 60% and widths in good agreement with the spatiotemporal coherence properties of the biphoton state. Moreover, we demonstrate that maxima of momentum spatial coincidences are evidenced within each image, in correspondence with these dips.

High Speed Imaging of Spectral-Temporal Correlations in Hong-Ou-Mandel Interference

“…It has become synonymous with HOM interference, but in reality this dip is only a single-mode representation of a far more complex multi-mode effect. Recent demonstrations of the HOM effect in spatial-temporal [11], and spectral-temporal [12][13][14][15] modes have revealed the complex multi-dimensional nature of HOM interference.…”

High-speed imaging of spatiotemporal correlations in Hong-Ou-Mandel interference

“…This is obtained by means of a vertically oriented Dove prism, implementing q y → −q y , and by a different parity in the number of reflections in the two paths (including the reflection from the BS), which corresponds to applying q x → −q x . An alternative approach b c a < l a t e x i t s h a 1 _ b a s e 6 4 = " 8 Y U 5 F L v W j 7 I Y X M j i T + n b B o N U u k U = " > A A A C y X i c d V F N b 9 N A E N 2 Y A i V 8 t X D k s q q F x C m y I w Q c q 3 K p x K W V S F s p t q r x Z p y s s r s 2 u + O 2 w f W p R 6 7 w R / g 3 / B s 2 r i v a p I y 0 0 t s 3 7 Q q u / g I T 8 u B k < / l a t e x i t > y < l a t e x i t s h a 1 _ b a s e 6 4 = " A q h X D x n B y z 8 r E 6 p 1 u + g + k 9 / V e / E = " > A A A C 2 n i c d V F N j 9 M w E H X D 1 1 K + u n D k Y h E h L Z c q q R B w X A E H j o t E d 1 e q o 2 r i T l q r t h P Z k 6 I q m w s 3 x J U j V / g B / B v + D W k 2 K 3 b b Z S R L z 2 / e e x 5 5 0 k I r T 1 H 0 p x f c u H n r 9 p 2 9 u / 1 7 9 x 8 8 f D T Y f 3 z s 8 9 J J H M t c 5 + 4 0 B Y 9 a W R y T I o 2 n h U M w q c a T d P l u 0 z 9 Z o f M q t 5 9 o X W B i Y G 5 V p i R Q Q 0 0 H A / E e N Q H X / E C Y k p s X 0 0 E Y D a O 2 + C 6 I O x C y r o 6 m + 7 3 f Y p b L 0 q A l q c H 7 S R w V l F T g S E m N d V + U H g u Q S 5 j j p I E W D P q k a k e v + f O G m f E s d 8 2 x x F v 2 s q M C 4 / 3 a p I 3 S A C 3 8 d m 9 D X t e b l J S 9 S S p l i 5 < l a t e x i t s h a 1 _ b a s e 6 4 = " A q h X D x n B y z 8 r E 6 p 1 u + g + k 9 / V e / E = " would be to exploit the transverse position correlations, which would require imaging the crystal plane on the BS (e.g., see [21]); however, the resulting visibility can be strongly affected by imaging imperfections. A detailed experimental setup is shown in Fig.…”

“…Two-photon interference has been previously investigated with spatial modes, e.g., Hermite-Gauss modes [17,32], Laguerre-Gauss modes [33,34], and position and momentum modes [21,23]. In these approaches, each spatial mode is scanned individually, or the spatial modes are measured simultaneously but with a poor timing resolution.…”

“…However, there is a strong interest in quantum optics applications involving a large number of modes: high-dimensional states exhibit large information capacity [18], provide better security thresholds in quantum communication protocols [19], and can be useful for reducing the noise in quantum imaging [20]. Recently, HOM interference with a high number of spatiotemporal modes, i.e., a million modes (∼ 10 6 ), has been reported [21] -with a HOM dip visibility of ∼ 60%.…”

“…Performing HOM measurements in the spatiotemporal domain requires very long data acquisition times, which often have limited accuracy. Either physical raster scanning of detectors [22] and apertures [23] are employed, or spatially resolved EMCCD cameras are used [21]. The former technique generally provides good timing but poor spatial resolution, while the latter gives good spatial resolution but poor timing and significant noise.…”