Efficient Generation of Generalized Binomial States in a Cavity

1
Efficient Generation of Generalized Binomial
States in a Cavity
CEWQO 2007 Central European Workshop on Quantum
Optics 2007 14th Edition, 1-5 June 2007, Palermo,
Italy Grand Hotel et Des Palmes
R. Lo Franco, G. Compagno, A. Messina, A.
NapoliDipartimento di Scienze Fisiche ed
AstronomicheUniversity of Palermo
2
Outline

• Introduction Generalized Binomial States (GBSs)
• Analogy with the Coherent Atomic States (CAS)
• Efficient Generation of GBSs in a High-Q Cavity
• About the implementation
• Conclusion

3
Introduction
Introduction ?

• Quantum field state engineering
• Quantum superpositions, Entanglement
• What kind of electromagnetic field states to be
  generated?

Investigation of Quantum Mechanics (QM)
Foundations
Application in Quantum Information Processing
4
Introduction ?

• Fock Number state
• The less classical state permitted by QM
• Coherent state
• The most classical state permitted by QM
• Fluctuations
  Non-orthogonal

What about intermediate non-classical states?
5
Generalized Binomial State (GBS)D. Stoler et
al., Opt. Acta 32, 345 (1985)
Introduction ?

• Normalized N-photon GBS defined as
• 0 ? p ? 1 ? probability of single photon
  occurrence
• f ? mean phase Vidiella-Barranco and Roversi,
  PRA 50, 5233 (1994)
• Interpolating between number and coherent state
• p 0 ? N, p,f? 0? p 1 ? N,
  p,f? N?
• N ? ?, p ? 0, Np a2 ? N, p,f? ? a
  aeif ?

6
Introduction ?

• Orthogonality property
  R. Lo Franco et al., PRA 72,
  053806 (2005)
• The GBS exhibits non-zero mean fields
• u(r) mode spatial distribution
• Moreover
• GBSs analogous to coherent atomic states (CASs)

7
Analogy between GBS and CAS
Analogy GBS CAS ?
z
N two-level (spin ½-like) atoms Dicke States
definite atomic excitation
v
u
q
y

• Coherent atomic states
  F. T. Arecchi et al.,
  PRA 6, 2211 (1972)

j
x
Orthogonality
8
Analogy GBS CAS ?
GBS
CAS
z
v
u
q
y
j
x
Orthogonal states
9
Angular momentum operators for GBSsHolstein-Prima
koff operators
Analogy GBS CAS ?
Along axis z (non-rotated) We find the rotated
angular momentum operators
Orthonormal basis of e.m. field states along
direction q,j
10
Analogy GBS CAS ?

• Analogies

Non-correspondent to the coherent states, as
usually meant!
11
Efficient generation of GBSs in a cavity
Efficient Generation GBS ?

• Analogy between GBSs and CASs
• Generate GBSs of angular momentum N/2 by
  interactions among e.m. field and N two-level
  (spin-like ½) atoms
• Pseudospin operators
• Appropriate framework Cavity QED (CQED)
  High quality factor
  and good atoms control
  J. M. Raimond et al., Rev. Mod.
  Phys. 73, 565 (2001)
• Generate GBSs by resonant interactions between
  cavity field and N consecutive two-level atoms.
• Proposed methods are conditional (Pgen 1/2N )
• M. Moussa and B. Baseia, Phys. Lett. A 238, 223
  (1998)

12
Efficient Generation GBS ?

• Find an efficient generation scheme in CQED
• Idea Look for appropriate atom-cavity
  interaction times!

C
D??
D??
R
N two-level atoms

• The Procedure we found
• Prepare opportune atomic states by the Ramsey
  zone R
• Take into account all the atom and cavity field
  free evolution times
• Choose different suitable atom-cavity interaction
  times (Jaynes-Cummings Model)
• Measure the final atomic states

13
Efficient Generation GBS ?

• Atoms measured in the ground state
• 
  Obtain cavity states of the kind
• 
  Fidelity

f f (j1 and free evolution times)
14
Generation and Detection of a GBS with N 2 R.
Lo Franco et al., PRA 74, 045806 (2006)
Efficient Generation GBS ?
C
T1 p/2g, T2 41p/4g
R
Generation
1
2
TP 41p/4g
Detection
D??
D??
Probe two-level atom
Rdecoding
15
About the implementation
Implementation ?

• Precise atom-cavity interaction times requested.
  
• Experimental error E. Hagley et al., PRL
  79, 1 (1997)
• Circular Rydberg atoms and superconducting
  cavities with quality factors Q 108 ?1010 ?
  
  Neglect atom and photon decays during the
  interactions
• Obtain different atom-cavity interaction times by
  (i) selecting different velocities or (ii)
  applying a Stark shift inside the cavity
• Non-perfect atomic detection does not sensibly
  affect the scheme (high generation probability).
• Promising result on high-efficiency atomic
  detection and sequence of definite atoms number
  E. Auffeves et al., PRL 91, 230405 (2005)

16
Conclusion
Conclusion ?

• Generalized Binomial States (GBSs) are the
  electromagnetic analogous of Coherent Atomic
  States.
• Generalized Binomial States with 1 N 10 can be
  efficiently generated by standard resonant
  atom-cavity interactions.
• The scheme is near to be realized in laboratory.
• Perspectives generate superpositions of
  orthogonal GBSs in a cavity or their entanglement
  in separate cavities ? Quantum-classical border
  investigation and quantum information
  applications.
• Application GBSs as reference state for
  measuring the canonical phase of a quantum field
  state Pregnell and Pegg,
  PRL 89, 173601 (2002) PRA 67, 063814 (2003)