Recording Quantum Fluctuations of Light in Atoms – Niels Bohr Institutet - Københavns Universitet

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We have studied the interaction between laser light and atomic spins, and we have concentrated on the noise aspect of the interaction. 		 



The experiment in short

The experiment is shown schematically below:

Exp setup principle

A probe laser is sent through a sample of oriented atoms. The optical and repump laser maintain the spin orientation and causes decay. A detection system measures the fluctuations of the light leaving the atomic sample. A constant magnetic field moves atomic fluctuations to the Larmor frequency.

One important question is, can we see the quantum projection noise of light and atoms? And on top of this, can we see the effect of light noise on atoms and vice versa?

The variables of interest are for atoms the transverse spin components Jy and Jz and for light the Stokes operators Sy and Sz given by 2Sy = flux(+45-pol) - flux(-45-pol) and 2Sz = flux(σ+-pol) - flux(σ--pol) describing polarization. We always have to a very good approximation a strong, classical 2Sx = flux(x) - flux(y) ≅ flux(x), and Jx can also be regarded as classical.

In absence of atoms we can indeed get to the quantum noise limit of light - also called the shot noise level. Furthermore, we may squeeze the polarization state of light such that the noise of the light fluctuations are reduced/increased with respect to the shot noise level. Mathematically, the noise of Sy and Sz is parametrized by εy and εz, where ε = 1 corresponds to the shot noise level, ε < 1 to squeezing, and ε > 1 to anti-squeezing.

In order to examine exchange of fluctuations between light and atoms, we must make clear what we expect to measure if all the noise is of quantum nature. We model this by calculating the interaction between light and atoms from the Faraday effect. In addition we assume that the transverse spin components Jy and Jz are subject to decay with a rate Γ. A calculation shows (see references for details) that the power spectrum Φ(ω) of the photocurrent i(t) is given by:

Theoretical spectrum

It is the Sy-component of light which is measured and reflected in the above equation. The first term is the initial noise of light which is proportional to εy. It also scales linearly with the total flux = 2Sx. The second term has a Lorentzian shape which reflects the fact that the noise emerges from atoms which have a memory characterized by the Lorentzian width. The resonance frequency Ω is the Larmor frequency of atoms. The parameter a describes the strength of the interaction. Inside the curly brackets, the first term is the pile up of quantum noise from light onto atoms. A calculation shows that the Sz component of light should feed into atoms, we see the signature of this by the εz parameter. We also call this term the back action term. The second term in the curly brackets is the initial quantum projection noise of atoms. It has the characteristic linear scaling with the spin size Jx. Now let us see some experimental data:

 

Two Lorentzians

An example of measured spectra. The solid line is obtained with the input light in a vacuum state (εy = εz = 1). When the input mode is in a squeezed state with εy < 1 and εz > 1 (dashed line) the Lorentzian part from atoms increases (back action term increases) while the wings decrease (first term in equation decreases). The peak on the right is technical noise.

Conclusion

The data above (and many other traces) show that we can really resolve the effect of quantum noise. Especially, atoms and light are sensitive to the projection noise of each other. This brings optimism for future quantum memory protocols in spin systems. In addition we learn many aspects of quantum interactions between light and matter. Our data agree with theoretical calculations to a high degree. Experimentally we can distinguish projection noise of light, projection noise of atoms, back action noise of light onto atoms, and additional technical noise sources. We also understand the decay mechanisms of the different noise fluctuations.

Further reading

  • C. Schori, B. Julsgaard, J. L. Sørensen, and E. S. Polzik,
    Recording quantum properties of light in a long-lived atomic spin state,
    Phys. Rev. Lett. 89, 057903 (2002).

  • J. L. Sørensen, B. Julsgaard, C. Schori, J. Hald, and E. S. Polzik,
    Quantum noise limited laser probing of atomic spin states,
    Laser Physics 13, 359 (2003).

  • J. L. Sørensen, B. Julsgaard, C. Schori, and E. S. Polzik,
    Quantum limits encountered in atomic spin measurements,
    Spectrochim. Acta B 58, 999 (2003).

  • B. Julsgaard, C. Schori, J. L. Sørensen, and E. S. Polzik,
    Atomic Spins as a Storage Medium for Quantum Fluctuations of light,
    Quantum Information and Computation 3, Special issue, 518 (2003).

  • B. Julsgaard,
    Entanglement and Quantum Interactions with Macroscopic Gas Samples,
    PhD-thesis, University of Aarhus (2003).