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Durham University

Quantum Light and Matter

Spectroscopy of Thermal Vapours

Thermal vapour spectroscopy is funded by STFC and the EPSRC Platform Grant 'Atom-based Quantum Photonics'

See also a brief summary of the projects in this video

Quantum Optics

Solar Filters

Magneto-optical Spectroscopy

Atomic Line Filtering

Narrow-band optical filters are used in a variety of applications in laboratories for filtering out a signal frequency over a crowded background. While the best thin-film interference bandpass filters have bandwidths of a few nanometres, using atomic media to create bandpass filters can yield bandwidths around 3 orders of magnitude smaller, while still retaining high pass-band transmission.

There has been much research focussing on atomic Faraday filters (often known in the literature as FADOF filters, though the acroynm is misleading), where a near-resonant atomic medium is placed between two crossed polarisers in the presence of an axial magnetic field. The axial magnetic field is responsible for the Faraday effect, a magneto-optic effect whereby the polarisation of light is rotated as it traverses a medium. The optical rotation can be engineered to be close to 90 degrees, leading to almost complete transmission in the pass-band.

Faraday filters have found many applications in and beyond atomic physics: they are used in solar observations, frequency stabilisation of dye lasers, remote temperature sensing, atmospheric LIDAR, diode laser frequency stabilisation, Doppler velocimetry, optical communications and quantum key distribution in free space, and quantum optics experiments.

We have been investigating atomic filtering in Durham for a number of years; some links to our published papers can be found on the publications tab.

How atomic line bandpass filtering works

For this example, we take the simplest atomic structure required for atomic line filtering. The most basic atomic level scheme where it is possible to observe Faraday rotation is the J=0 to J=1 system with 4 mJ levels (which can be realised in, e.g. Sr). Figure 1 shows the energy level structure of this system. In the absence of an applied axial magnetic field (dashed lines), the sub-levels of the J=1 manifold are degenerate and there is no preferred quantisation axis. All 3 transitions (J=0,mJ=0J=1,mJ=0,±1) can be driven.

Fig 1: Energy levels of the J=0 to J=1 system in the presence of a magnetic field

The application of an axial magnetic field has two effects. First, the energy level degeneracy is removed due to the Zeeman effect, which shifts the energy levels according to their mJ quantum number by an amount ℏΔB=mJμBB, where μB is the Bohr magneton. Second, the magnetic field axis now defines a quantisation axis. In the Faraday geometry, the magnetic field axis is aligned with the propagation axis of the light field. The electric dipole transition selection rules mean that only ΔmJ=±1σ± transitions can be driven (π transitions are forbidden), by the application of left/right circularly polarised light (Linearly polarised light can be decomposed into equal components of the circular basis and will drive both σ+ and σtransitions). Since the absorption and dispersion for each circular polarisation are displaced in frequency, the medium is both circularly dichroic and birefrringent, respectively. As shown in figure 1(b) the transmission of each polarisation component can be considered it's own 2-level system with it's resonance frequency shifted by ±ΔB, and with corresponding complex refractive indices (fig. 1(c)) n± associated with σ± transitions, respectively.

To calculate the total transmission, phase shift and optical rotation, one must propagate the electric field through the atomic medium. The two polarisation components experience a medium with different refractive indices, and so pick up a relative phase shift. A phase shift between circular components leads to a rotation of the plane of linear polarisaiton, given by ΔÏ•=(nRnL)kâ„“/2, where nR,L are the refractive indices associated with the σ± transitions (the exact coupling depends on whether the magnetic field vector points parallel or anti-parallel to the light wavevector).

Fig 2: Typical optical setup for Faraday filtering

This Faraday optical rotation is frequency-dependent, and when combined with a pair of crossed-polarisers as shown in fig. 2, this creates an optical bandpass filter with a distinctive spectral profile. A typical profile is shown in fig. 3 below. Off resonance, at large detuning, [region (i)] the atom-light interaction is negligible, there is no optical rotation, and the crossed-polarisers mean that no light is transmitted. In between the split lines [region (iii)] there is still a significant optical rotation, combined with very little absorption, so here the filter transmission is maximised. The optical rotation can be engineered through the amount of atom-light interaction (by changing the atomic density) so that there is approximately π/2 rotation at the peak, leading to a filter with very little loss. Where either circular polarisation is strongly absorbed [region (ii)], the total filter transmission is approximately 1/4, since half the linearly polarised input light is absorbed, leaving pure circularly polarised light, which is then attenuated by another factor of 2 by the second linear polariser.

Fig 3: Typical Faraday filter spectral profile

Applications of atomic line bandpass filters

Under construction!

Faraday laser...

Fig 4: Schematic of the Faraday laser design and testing setup. LD - Laser diode; PBS - Polarising beam splitter cube; PM - permanent magnet; M - partially reflecting mirror; PZT - piezo transducer; PD - photodiode; BS - beam splitter; FPD - fast photodiode.

Atoms, Lasers and Magnets

We investigate the interaction between alkali-metal atoms and light in large magnetic fields, where typically the Zeeman effect dominates over the internal atomic structure. In this regime, known as the hyperfine Paschen-Back regime, atomic transitions can be separated by more than the Doppler width, allowing individual 2-, 3- and 4-level atomic systems to be realised without the need for either optical pumping or laser cooling.

The Hyperfine Paschen-Back regime

In a weak external magnetic field, the nuclear spin I and the electron angularmomentum J couple to give the total angular momentum F; the latter and its projection onto the field axis, mF are good quantum numbers. Decoupling of I and J occurs for stronger fields, and these vectors precess independently about the magnetic field; their projections mI and mJ are the good quantum numbers in this regime. An estimate for the decoupling field, B0, above which the hyperfine Paschen–Back regime is achieved is given by B0=Ahfs/µB,where Ahfs is the ground-state hyperfine coupling coefficient, and µB is the Bohr magneton. For Rb, B00.25T.

Breit-Rabi diagram

Even at magnetic fields that are a significant fraction of a Tesla, the ground state of the alkali atoms does not completely decouple into the mI,mJ basis; the true state is a superposition of quantum numbers, as shown in the figure below.

We plot above the Breit Rabi diagram for the 5S1/2 state of 87Rb up to 0.5 T, with the state decomposition in the mI,mJbasis (L=mL=0⟹mJ=mS). Even at this large field there remains a small admixture of states, which gives rise to the 'weak' transitions in the spectra below.

Experimental realisation

Whilst small fields on the order of a few tens of mT (few hundred Gauss) can be generated with small conventional coils, to produce uniform fields of the order of 1 Tesla we use permanent NdFeB magnets.

The top-hat magnets, shown below, are able to generate a near-uniform (<0.1 mT) field of around 0.6 Tesla over the central 2 mm region when placed close together.

In this central reigon between the two magnets, we place our heated small vapour cells and investigate spectroscopic signals.

Transmission spectroscopy

The plot below shows the expected signal from a 1 Tesla transverse magnetic field, with the input polarisation at 45 degrees to the magnetic field axis such that σ± and π atomic transitions are driven. The plot below shows the same Breit-Rabi diagram, but for both the ground and excited states. The arrows show which transition comes from which group of states, and their position horiztonally corresponds to their frequency detuning (zero is defined by the weighted line-centre, so the spectrum appears to be almost symmetric).

For Rb87, excited on the D2 line, the spectra form six groups of four peaks. Two groups come from each of the σ± and πtransitions, and on the figure are labelled with red, blue and olive lines, respectively. As well as these strong transitions, there are also six groups of 3 'weak' transitions, which arise from the incomplete decoupling of the ground state into the mI,mJeigenbasis. In the central regions of the spectrum, these are almost degenerate (separated by the 5P state mI splitting, which is much smaller than the Doppler width) with the strong transitions, but in the extreme wings of the spectrum they appear by themselves.

Optical rotation signals

<Under construction>

Isolated multi-level systems

In the spectrum above, each transition is separated by more than the Doppler width, so even though this is a thermal vapour we can think of each transition as a separate two-level system. By adding more lasers that couple additional atomic states, we can address isolated 2-, 3- and 4-level systems.

Electromagnetically Induced Transparency

Electromagnetically induced transparency (EIT) occurs when ...

In the HPB regime, due to the isolation of a 3-level system, we can demonstrate text-book EIT signals, an example of which is below (taken from Whiting et al. PRA 2016).

Electromagnetically Induced Absorption

By adding to the optical setup a second coupling laser, which is counter-propagating to the first coupling laser, we can realise electromagnetically induced absorption, instead of transmission, which arises from multi-photon resonances. This would be impossible to visualise in a multi-level system, but in the HPB regime with our 3-level system this becomes clear. The plot below shows the EIA lineshape, and a fit to our data based on a mutli-photon absorption model (see Whiting 2015 Opt Lett for more details).

The top panel of the plot shows ...

Four-Wave Mixing (4WM)

<under construction>

Extremely high-field spectroscopy

Spectroscopy up to 8 T demonstrated in the Faraday geometry...


What is ElecSus?

ElecSus is a cross-platform software package developed over many years by members of the JQC. It calculates, in the weak-probe regime, the Electric Susceptibility of an atomic medium.

ElecSus is designed primarily for quantitatively predicting spectra of thermal vapour cells of Sodium, Potassium, Rubidium or Caesium, and fitting experimental data to theory. This facilitates the design of optical devices such as Faraday filters, optical isolators and circular polarisation filters.

How does it work?

We have written two papers about the features of ElecSus. They are both open-access and can be found here:


Example uses of ElecSus

Since version 2, we now include a graphical interface (GUI) for ease of use. This makes getting up and running producing spectra and fitting to experimental data much easier. A screenshot from the GUI is shown below:

Because ElecSus is fast to run, it can be used to make videos showing the evolution of various parameters. One of our main applications involves the Zeeman effect, which shifts atomic energy levels in an applied magnetic field. The videos below show how the optical transition frequencies (involving both ground and excited states) vary as the field is ramped up.

A video showing the emergence of the hyperfine Paschen-Back regime in a thermal Caesium vapour. The data for this video was produced using ElecSus.

Where can I get ElecSus?

ElecSus is hosted and maintained regularly on GitHub:

ElecSus on Github

Quantum Optics in Atomic Vapours

Four-wave mixing (4WM) in the hyperfine Paschen-Back (HPB) regime

In the absence of a magnetic field, multiple-path interference results in a 4WM signal that is complex and difficult to model. In the presence of a high magnetic field (0.6 T), entry into the HPB regime removes the interference and results in a "clean" 4WM signal which is readily modelled with 4-level Optical Bloch equations

Heralded single photons

Through a four-wave mixing (4WM) process in rubidium-87, we can generate heralded bichromatic single photons from an atomic collective spin excitation (CSE). The photon arrival times display collective quantum beats (see image below), a novel interference effect that results from the relative motion of atoms in the CSE.

Thermal Cs Rydberg

Strong Interactions in a High Number Density Rydberg Vapour

We use a 3-step excitation process to create Rydberg atoms in a Caesium vapour confined within a glass cell. By heating the cell, we can control the vapour pressure and the number density of excited atoms, and by measuring the fluorescence and transmission properties of the medium we can interrogate the strong interactions between the excited atoms.

The experiments are either pulsed (looking for transient effects) or continuous wave CW (exploring the steady states of the system). In the CW setup we find ‘intrinsic optical bistability’ where a hysteresis effect means that the medium has two distinct responses to the same stimulus. In the pulsed regime we measure ‘critical slowing down’ where the response time of the medium diverges as a first-order phase transition between the two bistable responses is approached. Although the optical bistability is a steady-state phenomenon, the system is far from equilibrium, as it is being driven and dissipating energy. Our experiment therefore provides an opportunity to study an unusual example of a non-equilibrium phase transition.

Nonequilibrium Phase Transition in a Dilute Rydberg Ensemble
C. Carr, R. Ritter, C. G. Wade, C. S. Adams, and K. J. Weatherill
Phys. Rev. Lett. 111, 113901 (2013)

We have demonstrated a nonequilibrium phase transition in a dilute thermal atomic gas. The phase transition, between states of low and high Rydberg occupancy, is induced by resonant dipole-dipole interactions between Rydberg atoms. The gas can be considered as dilute as the atoms are separated by distances much greater than the wavelength of the optical transitions used to excite them. In the frequency domain, we observe a mean-field shift of the Rydberg state which results in intrinsic optical bistability above a critical Rydberg number density. In the time domain, we observe critical slowing down where the recovery time to system perturbations diverges with critical exponent α=-0.53±0.10. The atomic emission spectrum of the phase with high Rydberg occupancy provides evidence for a superradiant cascade.

Thin Cells

Coming Soon....