PI at NU: Prem Kumar, Professor. Co-PI: Horace P. Yuen, Professor

Transcription

1 Multidiscilinary University Research Initiative Kick-o Meeting: June MIT/NU Collaboration on Quantum Inormation Technology: Entanglement Teleortation and Quantum Memory PI at NU: Prem Kumar Proessor Deartment o Electrical and Comuter Engineering Northwestern University Evanston IL Tel: (847) ; Fax: (847) ; kumar@northwestern.edu Co-PI: Horace P. Yuen Proessor Deartment o Electrical and Comuter Engineering and Deartment o Physics and Astronomy Northwestern University Evanston IL Northwestern University

2 Key Elements o MIT/NU MURI Entanglement teleortation and quantum storage using singlet states (mostly based at MIT) Entanglement and teleortation using ield quadratures (mostly based at NU) New aradigms or quantum communication and memory (based at both MIT and NU)

3 Singlet-based Teleortation and Quantum Storage One ho M L P L M M L P L M M L P L M Two hos B M Quantum memory P High brightness olarization-entangled hoton-air source B Bell state measurement L 5km; can reach 1km with two hos

4 Field-Quadrature based Entanglement and Teleortation in One ho out H L F L T H L F L T L T Quantum Teleortation Reeater Line F Source o entangled ield quadratures H Dual quadrature homodyne detection T Teleortation comletion via modulated mean-ield injection L km in Inut state out Teleorted outut state

5 Quadrature Entanglement and Teleortation using Solitons in Fibers Objective: Demonstrate iber-based teleortation o quantum states. Aroach: Use two time and olarization multilexed Sagnac iber loos to roduce quadrature-entangled beams. Delayed Pums PM Fiber Sagnac Loo PM 5/5 Couler X Cross Slice PM Fiber Delay Polarization Controller Dierential Phase Control Inut State 1.5 µm Fiber Laser HWP EPR Beam in PBS Homodyne EPR Beam 1 to Bob Homodyne 1 Alice's Measurement Station 1 km Fiber ~ Classical Inormation ~ Phase Modulator Amlitude Modulator Teleorted Ouut State out Bob's Measurement Station Northwestern University

6 Proagation o Light in a Noinear Otical Fiber Wigner QPD at the Inut (Coherent State) Im {u} Wigner QPD at the Outut (Number--Phase State) Im {u} u() Re {u} Noinear Otical Fiber o Length "z" u(z) Re {u} Noinear Schrödinger Eq. (moving rame o reerence): Solutions Quasi-CW ( β ): ( u T ) Linearized around Fundamental Soliton (β - negative): z u u β T + ( T z ) i γu ( T z ) u ( T z ) u ( T z ) u( T z) n e iγu + γ β β ( T z) sech T + u ( T z) e ( T ) u ( T ) z n γ β [ u( T ) + u( T )] n i γ z u(t) - ulse enveloe β - nd order linear disersion γ - noinear interaction constant Ave. number o hotons: Commutator: n + u ( T z ) u ( T z ) dt [ ] + u ( T z) u ( T z) δ( T T )

7 Quasi-CW Proagation (Linearization Aroximation) Exact mean o the ield-oerator (assuming coherent state inut): u ( z ) u ( ) e i u ( ) sin( γz ) e u ( ) (1 cos( γz )) z θmin For any reasonable roagation distance amlitude remains unsqueezed: Linearized Solution ( T ) (around ( ) e i u T ): Noinear length (hase-shit): z ( T ) L γ z u( T ) u( T) + b( T ) u ( T ) e i [ ] ( T) γ z Im {u} θmin Bogoliubov transormation (unitary µ ν 1 ): + b( ) µ u() + ν u µ 1 + i ν () i θmin Quadrature-noise gains: out in X + ν X X max out min ( ) in ( µ ν ) X µ max 1 + ± min g max/ min µ ± ν For g ± 1 >> 1 max/ min [ ] Re {u} Minimum uncertainty roduct or all T : X out min ( T ) X out max ( T ) 1 16 gmax ( T) gmin( T) 1

8 Noinear-Fiber Sagnac Intererometer (Quasi-CW Classical Descrition) Pum "P" Fiber Couler 5/5 U+ Fiber o Lengthz 5/5 Beam Slitter Signal "S" Pum "P" U+ Mirror U- U- Signal "S" Fiber Sagnac Intererometer s ( θ ) S Signal ower gain (i.e. ): S G s Mirror Mirror Ordinary Sagnac Intererometer P s ( θ ) P Pum ower gain (i.e. ): G Gs cos ( x ) + s sin ( x ) s sin( x )sin( θ ) s x x G cos ( ) + sin ( ) + s sin( x )sin( θ ) Noinear hase-shits: Pum: Signal: Cross: s x γ zp ( T ) γzs ( T ) s cos(θ ) Initial hase dierence iθ ( T ) (i.e. u ( T ) P ( T ) e ; u ( T ) S ( T iθ s ( T ) e ); θ ( T ) θ ( T ) θ ( T s ) s ) Note: Signal/um ower gains are noinear in P (T) & S o (T) and hase-sensitive.

9 Quantum Noise in Noinear-Fiber Sagnac Intererometer Im {u} Coherent State Inut u() Re {u} Pum "P" noise in Fiber Couler 5/5 U+ Noinear Otical Loo Mirror (NOLM) Fiber o Lengthz U- Im {u} Otical Fiber Lengthz Number-Phase State Outut Signal "S" noise out M. Rosenbluh and R. M. Shelby Phys. Rev. Lett (1991); K. Bergman and H. A. Haus Ot. Lett (1991). u(z) Re {u}

10 Guided Acoustic Wave Brillouin Scattering (GAWBS) Noise In a jacketed iber every acoustic mode has a line-width ( ω s π ) and the entire GAWBS sectrum sans the range o - 1 MHz. 1MHz Inut: Light Wave: Measured GAWBS sectrum (1 MHz um LPF at 7 MHz) 6 MHz di The three comressional waves create index variation: (m -radial n-azimuthal -longitudinal) n m n n m n e i( ω Normalized index variance: s s m n t km n z) θ m n ( r ) n n ηkt Mc s kt - energy in an acoustic mode c s - seed o sound M - total mass o iber η - hoto-elastic constant GAWBS may be cancelled by using a two-ulse hasesensitive detection scheme with short ( t < 1ns) time delay between the ulses [K. Bergman C. R. Doerr H. A. Haus and M. Shirasaki Ot. Lett (1993)]. θ+π t θ

11 GAWBS-Comensated Noinear Otical Loo Mirror balanced hotodetector N variable PBS couler M L K O J +/- lens HWP Signal Arm B heater D F A olarization controllers dierential hase control C heater F-center laser E Pum Arm G circulator hase control H ~5/5 I variable couler Sagnac intererometer PM iber 1 m

12 Exerimental Results Rel. Photocurrent noise (db) Rel. hotocurrent noise ower Power gain Rel. light noise ower Gain and Fano actor (db) (a) (b) Pum strength (dimensioess units) λ.6 db( η.44) λ max db max 1.7 db G s min min G s The two traces are not synchronized let-to-right 1.4 db 1.87 db Shot noise (De)amliied noise sin(θ ) Rel. signal hase Levandovsky Vasilyev and Kumar Ot. Lett (1999). Almost noiseless amliication NF.3dB comared to 1.dB or an ideal linear laser amliier. Bright sub-poissonian light

13 Soliton Proagation (Linearization Aroximation) GAWBS - scales with iber length and average ower (linear henomenon). Squeezing - scales with square o the iber length and eak ower. For ultra-short (emtosecond) ulses squeezing dominates GAWBS. Ultra-short solitons avoid ast temoral sreading maintain shae & high eak ower. P T const In a undamental soliton (P - eak ower T - ulse width). Normalization o NLSE: Linearized NLSE (dimensioess orm): T z T z β T a ( ) T γ β u( ) 1 a ( ) i a ( ) a( ) + + a( ) Linearized solution Fundamental Soliton (canonical orm): a ( ) a( ) + a ( ) a sech( ) e / i [ + a ( ) a ( ) ] δ( ) Commutation relation

14 Solution via Perturbation Exansion ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) { } θ π i n i s s c c i i i e V V d V e b a Ω Ω + Ω Ω Ω + Hermitian Oerators and Resective Modes Exress Perturbations o: H.Haus and Y.Lai J. Ot. Soc. Am. B (199) H.Haus W. Wong F. Khatri J. Ot. Soc. Am. B (1997) Linearized NLSE: ( ) ( ) a ia a a i a i a Exansion based on a Comlete set o Orthogonal Eigenmodes o Linearized NLS: Aroach Based on: () () () () ( ) ( ) Ω Ω c c n n V V V - Photon Number - Momentum (requency) - Continuum at requency Ω - Phase - Position (time) - Continuum at requency Ω () () () () ( ) ( ) θ θ Ω Ω s V s V V Projection based on orthogonality relation: () ( ) () d b V i i * Re Symmetric: () ( ) * Antisymmetric: () ( ) *

15 Asymmetric Sagnac Intererometer (Asymmetric NOLM) Im {a in } a sol n Fundamental soliton ( ω) πsech( πω ) â in Fiber Sagnac Intererometer Fiber Couler ( transmittance T ) agvd â out â sol Fiber o Length z a sol / a out a out Re {a in } To direct detection setu â gvd a out A LO e i n 1 T T 1 e T i ( ω + 1) i e i () e T a () T a b 1 out sol Outut mean ield Outut quantum noise gvd Exeriments: S. Schmitt et al. Phys. Rev. Lett (1998) dB; D. Krylov K. Bergman Ot. Lett (1998) dB. a gvd a + i sol T 1 T CW wave [ i / b ( )] e n n e sol CCW wave iω + i a gvd ( ω )

16 Noise Reduction in an Asymmetric NOLM Levandovsky Vasilyev and Kumar Ot. Lett (1999). Periodicity: /π Noise reduction is limited by (1-T) losses. (1-T) limit Without disersion With disersion

17 MURI Fellow: Polarization Entangled Photon Pairs using Microstructure (Holey) Fibers DSF Fiber Sagnac Loo Entangled Photons at λ 1 to Bob Initial exeriments with standard disersionshited iber Delayed Pums 5/5 Couler X Slice X Slice with o 9 rotation PM Fiber PM Fiber Polarization Controler X Slice Standard Fiber WDM 1.5 µm Mode-Locked Fiber Laser Entangled Photons at λ to Alice Main exeriments near 8nm wavelength will be with microstructure (holey) iber obtained rom Lucent

18 Wavelength-Tunable Picosecond Pulse Source or Ultrahigh Seed WDM Communications 1541 nm ML-EDFL Pr Serkland and Kumar OL 4 9 (1999). Signal Sectrum over Tunable Range -3 NFSI Pum Pi FS FPC S db FPC1 5 Grating PBS AL DSF S+I Wavelength(nm) Pulse Shae (Auto-correlation) Main Results with EDFL Puming: Signal wavelength tunable over 7nm. 3nm er channel total 4 WDM channels s FWHM ulse width which corresonds to 1 Gb/s NRZ transmission data rate 4 channels at 1Gb/s rovide total system caacity u to.4 Tb/s! Insensitive to um olarization Normalized Amlitud All iber device a comact and rugged source Time (s) Northwestern University

19 Classical FOPA Theory or CW Gain G s CW FOPA Gain Equations cosh δk ( gl) g + ( ) δ sinh g ( γp ) k δk γp + ( ks + ki k ) β m δk γp + ( ωs ω m! ( gl) m ) Gain (db) Theoretical Gain Gain curves o the FOPA Zero disersion wavelength 1537 nm um ower 5 W l 1535 nm l 1539 nm l 1541 nm Wavelength (nm) Modulation (A.U.) E-5 1 E-5 E-5 E-5 E-5 1E-5 1E-5 1E-5 8E-6 6E-6 4E-6 E-6 E Detuning (nm) Exerimental Gain Results The CW theory rovides insight into the interlay between FOPA gain and various exerimental arameters (um ower um and signal wavelength iber length iber disersion and noinearity and hase mismatch). Although accurate data is diicult to obtain over the entire gain bandwidth we see that our system is behaving as exected.

20 Fiber-otic Parametric Amliier (FOPA) Aaratus Princiles o Oeration FWM occurs between synchronous um signal and idler ulses within the Sagnac loo Phase matching is achieved by oerating near the zero disersion wavelength o the iber in the loo The um is iltered rom the signal and idler by adjusting FPC1 so that the loo mirror relects Polarization control or eicient mixing is achieved by adjusting FPC Signal and idler are detected searately by disersing them with a diraction grating Intensity [au] FWM Sectra Results Idler Pum Am. Sig. Unam. Sig Wavelength [nm] Simliied Schematic 3 m DSF lo1537 nm λ o Grating +/- Filter FPC1 5 6 db Pum Inut FPC Elect. Sec. Analyzer Signal Inut

21 Quantum Proerties o the FOPA Radiation Relative Noise (db) Exerimental Noise Reduction Results Photon correlation in a FOPA Gain Exeriment Theory (E.5) Within the strong undeleted um aroximation the FOPA is equivalent to a nondegenerate OPA. The exected noise reduction or such a system is then as in [Aytür and Kumar PRL (199)]. Theoretical Noise Reduction R 1 E+ E g 1 E overall detection eiciency J. E. Sharing M. Fiorentino and P. Kumar Observation o twin-beams tye quantum correlation in otical iber to be submitted to Otics Letters.

22 Fiber Characteristics Observations While gain as a unction o λ is diicult to measure gain as a unction o um ower is easily obtained Fitting theory with data indicates that the CW theory is adequate to describe our ulsed system We obtain exerimental values or the relevant iber arameters that are consistent with exectations Gain Gain vs. um ower with its to theory Signal Wavelength 1544 nm 1546 nm 1548 nm Lines Theory.3. Disersion vs. λ Data Line Trend Peak Pum Power [W] D {s/(nm km)}.1. λ o Fiber Noinear Coeicient γ 1.8 [kw m] Zero Disersion Wavelength λ o nm Wavelength (nm) Northwestern University

23 Multidiscilinary University Research Initiative Kick-o Meeting: June 1 13 MIT/NU Collaboration on Quantum Inormation Technology: Entanglement Teleortation and Quantum Memory PI at NU: Prem Kumar Proessor Deartment o Electrical and Comuter Engineering Northwestern University Evanston IL Tel: (847) ; Fax: (847) ; kumar@northwestern.edu Co-PI: Horace P. Yuen Proessor Deartment o Electrical and Comuter Engineering and Deartment o Physics and Astronomy Northwestern University Evanston IL Northwestern University