1. Introduction

One of the most exciting applications of the non-classical light has been its interaction with atoms. The theoretical activity in this area has been very high during the last decade¹. The experimental progress was initially restricted to passive probing of atomic samples with amplitude squeezed light demonstrating sub-shot-noise sensitivity of absorption measurements^2,3,4,5. Later the non-classical dynamics of an atom driven by squeezed vacuum in a two-photon^6,7 and four-wave processes⁸ has been demonstrated. The latter experiments are based on the existence of non-classical pairwise correlations of the excitation. These correlations significantly change the dynamics of the ladder excitation of an atom. However, for a single atom effect the ladder configuration seems to be the only one where the peculiarity of such non-classical excitation is relevant.

The situation changes dramatically when one considers an atomic ensemble. When quantum correlated fields can interact with different atoms, say in a V-configuration, the correlations of the field can be mapped onto the atomic ensemble creating non-classical pairwise correlations between the individual atoms. A strategy for such mapping based on the idea of complete absorption of quantum correlated light in an optically thick atomic ensemble has been recently proposed⁹. In ref.⁹ this strategy is utilized to develop a proposal for generation of spin squeezed states (SSS) of atoms via interaction with squeezed light. However, this approach is also promising as a method of quantum information storage in long living spin states of atoms.

In this publication we report our progress up to date in generating frequency tunable polarization squeezed light and in studying the interaction of this light with an ensemble of cold atomic spins in the excited state of Cs atoms trapped in a magneto-optical trap (MOT).

 

Figure 1. The magneto-optical Cs trap emitting blue fluorescence at 456nm. The blue spot to the right is a reflection from one of the vacuum chamber windows.

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2. Sub-shot noise polarization spectroscopy

The polarization squeezed light is first used as a probe to increase the sensitivity in an atomic spin measurement. As first demonstrated in ref.¹⁰ the sensitivity of the polarization interferometer can be enhanced beyond the standard quantum limit with squeezed light as the probe. In our experiment such light is produced by generating the second harmonic of the Ti:Sapphire laser and using the second harmonic (around 250mW) to pump a subthreshold optically parametric oscillator (OPO). Our best effort in tunable squeezed light generation around 920 nm so far is 68% of quantum noise reduction corresponding to 5dB of squeezing as reported in ref.⁵.

From the beamsplitter relations it is easily seen that the resulting probe field c, emerging from a polarizing beamsplitter recombining squeezed vacuum and a coherent field, is given by c = ae^iϕ+ib, where a is a coherent field and b is squeezed vacuum. Given that a and b are fields of orthogonal polarizations it is easy to show that c will consist of quantum correlated pairs of σ ⁺ and σ^- polarized photons provided we choose the phase ϕ right. The non-classical correlations lead to (ideally) noiseless phase relationship between the σ ⁺ and σ ^- components of the probe. As a result the probe has (ideally) the noiseless linear polarization which allows to measure a polarization change of the probe caused by the atoms with a sensitivity better than the standard quantum limit. An alternative picture of the polarization squeezing is to consider the polarization noise of the coherent state local oscillator as emerging from the vacuum fluctuations in the orthogonal polarization. By means of squeezing these vacuum fluctuations, we generate the resulting field with reduced polarization fluctuations.

 

Figure 2. The setup used in experiment. Only two of the five trapping beams are shown, and the doubling- and OPO cavities are not shown.

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The setup for this experiment is shown in fig. 2. This is to our knowledge the first time polarization squeezed light is used in atomic spin measurements¹¹. In the experiment we record the polarization rotation induced on the probe light due to spin orientation of the atoms being probed. To avoid the low frequency amplitude noise of the probe laser, we perform the experiment at radio frequency; Ω/2π = 3MHz. We use an acousto-optic modulator to apply 10% intensity modulation to one of the trapping beams resulting in a 3MHz modulation of the atomic spin. The polarization interferometer shown in fig. 2 consists of two Glan-Thompson prism polarizers (PBS1/2) of which the first one serves as a polarization filter and a beam recombiner. Two beams with orthogonal polarizations, one in a coherent state and another in a vacuum state, are overlapped and sent through a half wave retarder (λ/2) which rotates the polarization by 45°. In the absence of any anisotropic medium (such as the trapped and spin polarized atoms) the second polarizer PBS2 will split the beam into two equally powerful beams which are detected by two pin silicon photodiodes (PD1/2). Our photodetectors are optimized for maximum response at Ω/2π = 3MHz where we have a shot noise level of 10dB above the electronic noise for the applied 100μW of optical power. The photocurrents i _1,2 are subtracted to produce the resulting photocurrent i- at the hybrid junction (HJ) and the output is sent into the RF spectrum analyzer (SA). With the spin polarized atoms present, the probe polarization will be rotated by an amount proportional to the spin orientation. This rotation gives unequal powers in the two output arms of the interferometer, and the difference current contains a signal proportional to the rotation angle.

Due to propagation losses from the MOT windows, polarizers and waveplates, our squeezing degrades as compared to the 5dB in ref.⁵. As a result we get 3.0dB of quantum noise reduction for our probe in the polarization interferometry experiment. When scanning the Ti:Sapphire frequency across the atomic resonance, the relative phase ϕ between the squeezed vacuum and the coherent state recombined on PBS1 must be kept fixed. This is done by a mirror mounted on a piezoelectric transducer, but due to the finite bandwidth of the servo loop locking the phase we loose another 0.5dB of squeezing leaving about 2.5dB or 44% quantum noise reduction for interferometry.

The target for our polarization squeezed light is a cold sample of Caesium atoms trapped in a magneto-optical trap¹² in which about 10^{6 133}Cs atoms with a density of a few times 10⁹cm^-3 are trapped with five trapping beams driving the 6S _1/2(F = 4) → 6P _3/2(F = 5) transition. With a temperature of about 100μK these atoms provide a dense Doppler free target for the probe. The trapping laser is an external cavity stabilized SDL 5401 laser diode with a single frequency output up to 45mW at 852.36nm. 30mW of this power is available for trapping. This laser field is responsible for both trapping and pumping of the three level ladder system (insert in fig. 2). Due to the hyperfine splitting of the ground state of ¹³³Cs a dedicated repumping laser is necessary for the MOT to avoid pumping of the atoms to the 6S _1/2(F = 3) state. A diode laser similar to the trapping laser is used for this purpose as well. The probe laser is a single frequency Ti:Sapphire (MBR-110 from Microlase) providing frequency tunable light at 917.49nm with a linewidth of 50kHz. The probe is near resonant with the 6P _3/2(F = 5) → 6D _5/2(F = 6) transition and probes the distribution of atoms in 6P _3/2. The 6D _5/2 state has a small probability for decaying to the 7P _3/2, which can further decay to the ground state emitting the blue fluorescence. With a strong probe, the blue light becomes visible as shown in fig. 1. By unbalancing the two horizontal and counter-propagating trapping beams, we can create a non-isotropic sample of (slightly) spin polarized atoms.

When the laser is scanned across the resonance a double-peaked structure due to spin modulation at 3Mhz is observed^13,14. The off-resonant noise level is given by the shot noise of the probe. By applying the polarization squeezed probe we reduce the quantum probe noise and improve the S/N by 2.5dB¹¹.

3. Squeezing of the quantum atomic spin noise

On our way towards the spin squeezed atoms, we have performed a series of experiments showing that we can actually reach the quantum limit of the atomic spin noise¹¹. To identify the quantum spin noise we use the following expression for the different noise contributions to the power spectrum component at frequency Ω of the detected difference current i _- for an optically thick medium_13,11:

Here ζ^E,C,Q are appropriate constants leaving explicit only the dependence on optical depth α (proportional to the number of atoms), photocurrent in the absence of atoms i ₀, the detection bandwidth B and the degree of squeezing of the probe ξ. The first term describes the broad band electronic noise of the detection system, second term is the light noise (shot noise for ξ = 0), third term is the noise/signal in case of classical modulation and the last term is the quantum noise due to stochastic fluctuations of the independent spins. Hence the quantum spin noise is identified as the noise contribution proportional to αe ^-2α and quadratic in the probe power.

The setup used in these experiments is very similar to fig. 2, except that we do not apply squeezed vacuum to our probe. Also, to avoid classical noise due to the well known phase noise in diode lasers¹⁴, we use a home built Ti:Sapphire laser for trapping. With this laser we are able to create an optically thick trap for the resonant 917nm probe which is critical to observe the quantum spin noise. If the atoms were merely passive absorbers, we would expect the noise level recorded on the SA to be reduced at resonance since the transmitted power and hence shot-noise is diminished. But due to the quantum spin noise we do not have the noise reduction as large as for a passive absorber. The additional noise introduced in the probe by atomic spin fluctuations is up to 20% of the shot noise level for our experimental conditions, and is therefore easily detected. Various checks have proved that we indeed have reached the fundamental limit of the spin noise set by fluctuations of the uncorrelated individual spin¹¹.

The fact that we have reached the quantum limit of the spin noise, which as the noise in the coherent spin state goes as the square root of the number of atoms, puts us in a position to implement the recent proposal on generation of spin squeezed states of atoms⁹. The proposed setup for generation and observation of spin squeezed states (SSS) of cold atoms is shown in fig. 3. SSS is generated in this proposal via interaction between an atomic sample and a normal Gaussian beam of squeezed light. The V-atoms (see the insert in the fig. 3) are excited with squeezed light, which leads to the spin squeezing within a closely positioned pair of final states with no allowed optical transition between them. Spin squeezing within a close pair of atomic states is, in fact, the situation relevant for precision spin measurements in frequency standards, magnetometers, etc. The light absorption process creates an entanglement of the field and the individual atoms, and when all the light is absorbed in the sample we realize a multiparticle entanglement, which as we shall show is only partly deteriorated (50 %) by the effect of atomic spontaneous emission. We stress that considering spin squeezing within the final states of the transition is crucial because the large initial state population of atoms provides a dominant non-squeezed contribution to the collective optical atomic coherence: in our proposal squeezing is obtained within an excited state manifold, and only atoms that have absorbed the quantum correlated light to get there contribute to the spin noise.

 

Figure 3. Setup used for generating and probing spin squeezed atoms.

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In our proposal SSS are generated for atoms in the final states of the transitions driven by quantum correlated excitation (states 1, 2 in fig. 3). To observe it we need to address only these atoms in our measurement procedure. This is exactly what occurs in the polarization noise measurement described in the previous section of the paper. Levels 0,1, 2 are now specified to be magnetic sub-levels. For Cs level 0 is the extreme sub-level of the ground state m = - F, levels 1, 2 are sub-levels of the 6P _3/2, F́ = F + 1 excited state. The coherent and the squeezed component of the quantum exciting field is now σ ^- and σ ⁺ polarized respectively. Excitation from other magnetic sub-levels of the ground state can be neglected due to optical pumping by the coherent component of the excitation. The pseudo spin components⁹ F_x,y now correspond to certain components of the alignment tensor $F_x=\frac{1}{2}\left(F_{\mathrm{1,2}}+F_{\mathrm{2,1}}\right)\propto T_{-2}^2+T_2^2\mathrm{and}{F}_y=-i/2\left(F_{\mathrm{1,2}}-F_{\mathrm{2,1}}\right)\propto T_{-2}^2-T_2^2$. To measure, e.g., F_y a probe linearly polarized along x is analyzed with a polarizing beamsplitter oriented at 45° to the x axis rendering the intensities I(45⁰) and I(135⁰). For the resonant probe I _- = I(45⁰) - I(135⁰) = αI ₀γ¹ F_y where α is a constant proportional to the optical depth of the medium, I ₀ is the probe intensity and γ¹ is the width of the transition. Obviously, quantum noise of I _- is determined by the quantum noise of F_y. When no squeezed vacuum is present a certain spin noise level proportional to the square root of the number of atoms is present on the top of the shot noise of the probe as observed in ref.¹¹. When the squeezed vacuum with appropriate phase is present as shown in fig. 3 F_y becomes squeezed and this noise level drops below the level set by the coherent spin state fluctuations demonstrating the SSS of the atomic ensemble. Adding half-wave retarders allows to perform this experiment with off-resonant probe.

4. Summary and conclusions

We have outlined the experimental and theoretical results on interaction of frequency tunable polarization squeezed light with cold atomic spins. Using such light as a probe we have demonstrated sub-shot-noise polarization interferometry with cold atoms. We have also shown how such light can be used to create non-classical correlations between the individual atomic spins leading to generation of the spin squeezed state (SSS). Recent results on fundamental spin noise observation in a MOT show that observation of the SSS may be within experimental reach.

Further research on interaction of non-classical light with cold spins will take even more exciting turn if mapping of the correlations/entanglement of such light can be performed with long-living spin systems. Utilizing complete absorption of quantum correlated fields via a Raman-type process one can, in principle, store quantum correlations in the ground spin state of atoms¹⁵. Keeping those atoms in, e.g. a magnetic trap can provide suitable conditions for the storage.