Statistics of Heralded Single Photon Sources in Spontaneous Parametric Downconversion Nijil Lal C.K. Physical Research Laboratory, Ahmedabad YouQu-2017 27/02/2017
Outline Single Photon Sources (SPS) Heralded Single Photon Sources (HSPS) and Spontaneous Parametric Downconversion (SPDC) Statistics of classical and non-classical sources of light - Observation of sub-poissonian statistics in SPDC - HSPS Study of second order correlation function
Single Photon Sources Why Single Photon Sources? Photon qubits : light-speed, loss-less, easy to manipulate Quantum Cryptography protocols demand Single Photon Sources generation of truly random numbers Single Photon Sources elementary excitation state of Em field, monochromatic, on-demand Quantum dots, Single atoms/ions, Color centres etc. 100% one photon, 0% multiple photons Experimental challenge weak coherent pulses but still not non-classical Solution : Heralded SPS!
Heralded Single Photon Sources Interaction with Non linear media Intense electric field causes redistribution of atoms, leaving them polarized P i = ε 0 (χ 1 ij E j + χ 2 ijk E j E k + χ 3 ijkl E j E k E l + )
Heralded Single Photon Sources Interaction with Non linear media Two pump photons ( ) annihilate to give an output photon of 2 P i = ε 0 (χ 1 ij E j + χ 2 ijk E j E k ) for a pump field, E = A cos ( t) P = ε 0 (χ 1 A cos ( t) + 1 2 χ 2 A 2 ( 1 + cos 2 t )) - Second Harmonic Generation from to 2 pump photon upconverted photons
Heralded Single Photon Sources Spontaneous Parametric Down Conversion Pumping a crystal with χ (2) nonlinearity generates a pair of signal and idler photons destruction of one photon (2 ) into two photons ( ). - Down Conversion
Heralded Single Photon Sources More on Spontaneous Parametric Down Conversion interaction Hamiltonian should take the form, H int ~ χ 2 p s i + h.c. Type-I BiO BiBO s, k s ħ p = ħ s + ħ i p, k p Nonlinear crystal i, k i k p = k s + k i Phase Matching Condition
Photon Statistics Electromagnetic field as a quantum harmonic oscillator. X 2 1/2 Coherent State, α = e α 2 2 α n n! n α 1/2 n=0 variance ( ) 2 = α (n n) 2 α = n - Poissonian X 1 Phasor diagram The Mandel Q-paramter, ( 2 ) = ( ) 2 1 = σ2 μ 1
Photon Statistics Type of Statistics Examples I (t) Variance and Mean Super-Poissonian Thermal, Chaotic, or Incoherent Time varying σ 2 > μ Poissonian Coherent light constant σ 2 = μ Sub-Poissonian Non-classical constant σ 2 < μ Sub-Poissonian statistics is a clear signature of non-classical nature of our source
Building Number Statistics Using an Oscilloscope The pair of photons generated in SPDC are coupled for maximum efficiency in signal (s) and idler (i) and the detection output is recorded using an oscilloscope. 405 nm -> two 810 nm coincidence window (τ c =1 ns) and interference filters help in selecting out the corresponding pairs. Lenses and Fiber Couplers are used to efficiently couple these photons to MultiMode Fibres.
Building Number Statistics Using an Oscilloscope Signal/ CRO Output Binary Converted Signal Bin size is varied in order to accommodate different average number of photons per bin. Binning 1 1 0 1 1 1.25 Building the statistics 1.00 The two-fold correlation between arms i and s, confirms that the twin photons are reaching the detectors simultaneously. g (2) 0.75 0.50 0.25 0.00-15 -10-5 0 5 10 15 (ns)
P(n) P(n) Building Number Statistics Using an Oscilloscope Thermal light, Q = 0.28 0.40 0.35 = 1 2 = 1.28 = 2 2 = 2.57 = 3 2 = 3.82 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0 1 2 3 4 5 6 7 8 9 10 n 0 1 2 3 4 5 6 7 8 9 10 n 0 1 2 3 4 5 6 7 8 9 10 n Heralded single photon source, Q = -0.08 0.40 = 1 0.35 2 = 0.92 = 2 2 = 1.84 = 3 2 = 2.77 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0 1 2 3 4 5 6 7 8 9 10 n 0 1 2 3 4 5 6 7 8 9 10 n 0 1 2 3 4 5 6 7 8 9 10 n
Building Number Statistics Using an Oscilloscope The number distribution for the parametric fluorescence from an individual arm shows super-poissonian statistics with Q = 0.28. The heralded counts follow sub-poissonian distribution with a significantly negative value for Mandel Q-parameter (Q = 0.08). The number distributions follow the same statistics for different values of average photon numbers.
HBT and Second Order Correlation Function, g (2) (τ) classical second order correlation function, g (2) (τ)= E t E t+τ E t+τ E t E t E t 2 D 1 for photons, g (2) (τ)= n 1 t n 2 t+τ n 1 t n 2 t+τ g (2) (0) = ( = 1 + ( )2 2 D 2 Counter for coherent sources, g (2) (τ) = 1 g (2) (0) = 1 for thermal sources, g (2) (τ) > 1 g (2) (0) = 2 for single photon sources, g (2) (τ) < 1 g (2) (0) = 0
Second Order Correlation Function, g (2) (τ) 405 nm HWP i IF FC MMF 1 SPCM 1 M 2 BiBO at the beamsplitter (BS), signal (s) photons will choose either s 1 or s 2. s BD BS IF FC s 2 s 1 IF FC SPCM 3 SPCM 2 triple coincidence between the detection of i, s 1 and s 1 photons are recorded. NS delay IDQ TDC g (2) (i,s1,s2) = C i,s1,s2 C i,s1 C i,s2 R C i,s coincidence counts between i & s R pair production rate
Second Order Correlation Function, g (2) (τ) Second order correlation function, g (2) (τ) is determined for signal (s) photons conditioned by the detection of idler (i) photons. g (2) (τ) for the heralded single photon source shows the expected HBT dip at zero delay. g (2) (o) = 0.07 anti-bunching has been confirmed, and quality of the single photon nature of the heralded source is determined. g (2) 1.0 0.8 0.6 0.4 0.2 0.0-8 -6-4 -2 0 2 4 6 8
( ) Second Order Correlation Function, g (2) (τ) 0.08 0.07 0.06 60 55 50 45 60 mw 7.5 mw g c (2) 0.05 0.04 0.03 0.02 0.01 N i,s1,s2 40 35 30 25 20 15 10 0.00 0 10 20 30 40 50 60 Power (mw) 5 0-6 -4-2 0 2 4 6 delay (ns) g (2) (o) improves from 0.064 to 0.0075 by reducing the power as a result of reduced number of multiphoton emissions
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