QUANTUM LIGHT :! A BRIEF INTRODUCTION!

Transcription

1 Quantum Physics QUANTUM LIGHT : A BRIEF INTRODUCTION Philippe Grangier Laboratoire Charles Fabry de l'institut d'optique, UMR 85 du CNRS, 927 Palaiseau, France Quantum Physics * Alain Aspect, in «Demain la physique», Ed. Odile Jacob, 24

2 Single Photon Sources clic clic clic clic «Photon gun»? A usual light source emits 2 photons per second How to get only one at a time? NV center : Single nitrogen atom embedded in diamond NV-Centers in diamond Experimental Setup QIPC / S4P a.u. QIPC / S4P ZPL Confocal Microscope CW or Pulsed Excitation Emission g(2)(#) Spectrometer Delay Absorption 637nm 75nm y Dichroic mirror x Pinhole Ø Time -toamplitude converter Bulk or Nanocrystals Ø = 5 nm << /n n = 2.4 m.5 mm Advantages : Less background Better collection Easier to handle Filters NA.3 z Diamond sample 5/5 Beamsplitter Avalanche photodiodes Photon Counting Antibunching : after detecting a photon, it takes some time to detect another one

3 Checking that there is one photon only Single Photon Interferences Single Photon Source : NV centers in diamond nanocrystals. Pulsed excitation: train of single photon pulses Experiment done at ENS Cachan : V. Jacques, E Wu, T. Toury, F. Treussart, J.-F. Roch. The polarization of a single photon carries a quantum bit or qubit 45 = ( h + v )/2 35 = ( h - v )/2

4 Quantum Information Main topics The characters Public key cryptosystems Rivest, Shamir et Adelman (RSA, 978) Eve # encoding Alice Bob P= a $b? What is inside the «public key»? the product P of two large numbers : factorization very difficult to perform

5 Factorising RSA 55 (52 bits - summer 999) «Challenge» proposed the RSA company ( Previous record : RSA4 (465 bits), february 999 «Challenges» proposed by the company RSA RSA55 = \ \ ; RSA55 is not a prime (probabilistic algorithm, very fast) Factorization? Preparation :9 weeks over workstations. Sieve : 3.5 months over 3 PCs, 6 countries Result : 3.7 Go, stored in Amsterdam Processing : 9.5 days on Cray C96, Amsterdam Factorization: 39.4 hours on 4 workstations f = \ ; f2 = \ ; f and f2 are primes, and f * f2 = RSA55 (immediate onpc) Improvement by two orders of magnitude between 999 and Problems : PUBLIC KEY CRYPTOSYSTEMS - Mathematical demonstrations about PKC have a statistical character (the factorisation may be found easily for unfortunate choices of a, b) --> recommendations for the choice of the prime numbers a and b - No absolute demonstration for security -> better computers, better algorithms (obviously kept secret)? - Article by Peter Shor (994) : a quantum computer might be able to factorize the prod uct of two prime numbers in a polynomial time lot of reactions Best classical algorithm (number field sieve) : nfs[n] = Exp[.9 Log[n] /3 Log[Log[n]] 2/3 ] nfs[2 24 ] / nfs[2 52 ] = Shor algorithm : shor[n] = Log[n] 3 shor[2 24 ] / shor[2 52 ] = 8 + Secret key cryptosystem : one-time pad (G. Vernam, 97) secret channel # = # Eve classical channel # Demonstrably secure if the key is : random as long as the message used only once (Shannon) # + =

6 + = Quantum Secret Key Cryptosystem : Bennett-Brassard (984) # $ % & quantum channel $ classical channel # + # Demonstrably secure if the key is : random as long as the message used only once (Shannon) unknown by Eve : Quantum laws = Coding basis Coding basis Sent bit Sent bit Reading basis Reading basis Received bit Received bit Discussion Sifted key

7 Industrial Perspectives? QUANTUM CRYPTOGRAPHY : PRINCIPLE (C. Bennett and G. Brassard, 984) QIPC / S4P Eve has to make a measurement without knowing the basis used by Alice ( this information comes too late for her ) All such measurements - intercept / resend using either the + or x basis will create errors in the - intercept / resend using an optimized basis (22.5 ) transmission - use quantum non-demolition measurements ( the more Eve knows, the - duplicate (clone) photons and keep one aside more errors ) * Evaluation of errors : After the initial exchange between Alice and Bob measure the error rate by comparing publicly a part of the raw key: -> evaluation of the amount of information (maybe) available to Eve. * Classical post-processing (essential for security ) Requires a public authenticated channel * Alice and Bob have a totally secure and errorless secret key (non-zero size if initial QBER < %) * Several startups worldwide are selling QKD systems (optical fibers, 5 km) The key to future-proof confidentiality IdQuantique (Genève) MagiQ Technologies (New York) * Intense activity in the USA (mostly military) and in Japan (NEC, Fujitsu ) * In Europe «Integrated Project» SECOQC : «Secure Communication based on Quantum Cryptography». Urban networks demonstrated in Vienna (28) and Tokyo (2) Quantum cryptography with satellites 44 km between LaPalma and Tenerife

8 Main topics Next steps...

9 Einstein, Podolsky and Rosen «paradox» (EPR-Bohm version) Source S emitting pairs of photons and 2 in the quantum state : ( x x2 > + y y2 >)/#2 Entangled state - The result is random for each photon, but measuring one polarization allows one to know the polarization of the other photon with probability unity. Bell s inequalities «Hidden variables» or «supplementary parameters» denoted, with a normalized statistical distribution %() : &d % () = '(, () = ±, '2(, (2) = ±, E((, (2) = &d % () '(, () '2(, (2) locality then : - 2 $ S $ 2 with : S = E((, (2) + E((', (2) + E((', ('2) E((, ('2) Demonstration : '(, () '2(, (2) + '(, (') '2(, (2) + '(, (') '2(, ('2) '(, () '2(, ('2) = ± 2 locality / freedom of choice - The measured polarization can be chosen arbitrarily, while the two photons are very far apart : what is «really» the polarization of the second photon? ( ( 2 (' For the indicated angles one has SQM = 2#2 Einstein, Podolsky and Rosen «paradox» (935) 22 5 (' 2 Conflict Experimental result? J= Dyelaser 55 nm Krionlaser nm J= Orsay s source of pairs of entangled photons (98-82) 2 { +, +, + } { x,x + y, y } = 2 J= r=5ns Emission of two entangled photons by an atomic cascade. * Laser-induced two-photon excitation of a cascade in a Calcium 4 atomic beam. ' detected pairs per second % precision for s counting * Random switching of polarizers Experimental tests of Bell s inequalities Experiments with an active fast change in the polarizers orientations (initially proposed by Alain Aspect in 976 to close the «locality loophole») Orsay 982 : A. Aspect et al, Phys. Rev. Lett. 49, 84 (982). * distance between polarizers : 5 m -> L/c = 5 ns * measurement switching time : 2 ns (ok) * violation of Bell s inegalities by 6 standard deviations (5 h counting time) Innsbruck 998 : G. Weihs et al, Phys. Rev. Lett. 8, 539 (998). * distance between polarizers : 4 m (optical fibers) -> L/c =.3 µs * truly random and independant switching time * violation of Bell s inegalities by 3 standard deviations ( s counting time). La Palma-Tenerife 2 : T. Scheidl et al, Proc. Natl. Acad. Sci. 7, 978 (2). * distance between polarizers :44 km (free space) -> L/c = 48 µs * truly random and independant switching time + %() independant of ( and (2 * violation of Bell s inegalities by 6 standard deviations (6 s counting time). Conclusion : Bell s hypothesis are untenable entangled states do exist

10 QUANTUM COMPUTING LINEAR ION TRAPS QUANTUM COMPUTER IN SILICON * Confinement using electromagnetic fields : «chain» of trapped ions Qubit : magnetic moment of phosphorus atoms individually implanted below electrodes B (= 2 Tesla) T= mk * Laser cooling : ions in the ground state of the harmonic trap A-Gates J-Gates A : qubit gates J : 2 qubits gates Barrier * Technically possible Silicium * Decoherence??? e- e- 3P+ 3P+ ~ 2 Å B. E. Kane, A silicon-based nuclear spin quantum computer, Nature, Vol. 393, p. 33, 998 Substrate Image of fluorescence from 8 ions in a trap Isolated ions in vacuum : decoherence much smaller than in a solid...

11 «Quantum Byte» (Innsbruck, 25) Quantum register with 8 qubits Preparation and read out: = Control of the «calculation» using a sequence of laser pulses 8 ( Difficult to draw As a conclusion... )