Influence of thermal effects on atomic Bloch oscillation

doi:10.1007/s11467-024-1420-9

Front. Phys.

2024, Vol. 19

Issue (6) : 62201 https://doi.org/10.1007/s11467-024-1420-9

Influence of thermal effects on atomic Bloch oscillation

Guoling Yin¹, Chi-Kin Lai², Nana Chang^2,³, Yi Liang², Dekai Mao², Xiaoji Zhou^1,^2,³(

)

¹. State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
². State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electronics, Peking University, Beijing 100871, China
³. Institute of Carbon-based Thin Film Electronics, Peking University, Taiyuan 030012, China

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Abstract

Advancements in the experimental toolbox of cold atoms have enabled the meticulous control of atomic Bloch oscillation (BO) within optical lattices, thereby enhancing the capabilities of gravity interferometers. This work delves into the impact of thermal effects on Bloch oscillation in 1D accelerated optical lattices aligned with gravity by varying the system’s initial temperature. Through the application of Raman cooling, we effectively reduce the longitudinal thermal effect, stabilizing the longitudinal coherence length over the timescale of its lifetime. The atomic losses over multiple Bloch periods are measured, which are primarily attributed to transverse excitation. Furthermore, we identify two distinct inverse scaling behaviors in the oscillation lifetime scaled by the corresponding density with respect to temperatures, implying diverse equilibrium processes within or outside the Bose−Einstein condensate (BEC) regime. The competition between the system’s coherence and atomic density leads to a relatively smooth variation in the actual lifetime versus temperature. Our findings provide valuable insights into the interaction between thermal effects and BO, offering avenues for the refinement of quantum measurement technologies.

Keywords Bloch oscillation optical lattice thermal effects cold atoms Raman cooling

Corresponding Author(s): Xiaoji Zhou

Issue Date: 24 May 2024

Cite this article:

Guoling Yin,Chi-Kin Lai,Nana Chang, et al. Influence of thermal effects on atomic Bloch oscillation[J]. Front. Phys. , 2024, 19(6): 62201.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-024-1420-9
https://academic.hep.com.cn/fop/EN/Y2024/V19/I6/62201

Fig.1 Experimental setup for both acceleration and gravity-driven BO. (a) Longitudinal movement of atoms in the 1D accelerated optical lattices under gravity, illustrating the periodic potential aligned with gravity in

x

-axis, depicted as a black arrow, and atoms with a pancake-shape spatial distribution. The acceleration of the optical lattice is achieved by modulating the frequency difference

δ ω = k α t

between the two lattice beams, as indicated by the two red arrows. In the co-moving frame, atoms are subject to a net force

m (g ? α)

. The longitudinal length

l / /

and lattice constant

d

are displayed in the figure. (b) Schematic diagram of the setup, illustrating the atoms are prepared within a crossed 1064 nm optical dipole trap. It highlights the Raman and lattice beams in the vertical direction, including the counter-propagating configuration achieved by reflecting one of the Raman beams. The downward lattice beam is combined with Raman beams in the same optical fiber, while upward lattice beams are merged with one Raman beam using a polarizing beam splitter (PBS) and two half-wave plates (HWPs).

Fig.2 Experimental sequence for the accelerated optical lattice. (a) Initial state preparation begins at

t 0

with atoms in

| F = 1 ?

. At

t 1

, a microwave pulse transitions atoms to

| F = 2, m F = 0 ?

, while atoms still in

| F = 1 ?

are removed using a state-specific clear beam. The first Raman pulse at

t 2

narrows the velocity distribution and transfers atoms to

| F = 1, m F = 0 ?

. Any remaining atoms in

| F = 2 ?

are then cleared. The optical lattice operation commences from

t 3

t 4

, ending with a second Raman pulse at

t 5

for velocity measurement by transferring resonant atoms to

| F = 2, m F = 0 ?

, followed by fluorescence detection at

t 6

. (b) The sequence for the accelerated optical lattice is detailed further: The lattice depth is linearly increased to

V 0 = 15

Er within

t r i s e = 1

ms and is maintained during

t h o l d

. Phase modulation initiates by synchronizing the lattice’s velocity with the atoms’ free fall, adjusting the lattice frequency difference

δ ω

at a rate of

k g

. To induce BO,

δ ω

is modulated at a rate corresponding to

α = ? 2 g

. Finally,

δ ω

is adjusted at a rate of

k g

to ensure zero relative velocity between the lattice and the atoms, facilitating mapping of the atoms’ states into quasimomentum space.

Fig.3 BO process in the co-moving frame. (a) Illustration of BO driven by a constant acceleration

g ? α

in the co-moving frame, showing atoms initially in the ground state (

q = 0

at the instantaneous S band). Subject to a constant force

F = m (g ? α)

, the atoms’ quasimomentum increases linearly until reaching the boundary of the first Brillouin zone. This induces Bragg scattering, resulting in quasimomentum shifts of

2 ? k

. (b) The BO process is depicted by black dashed arrows for the trajectory and red ellipses for atoms, corresponding to the momentum distribution of atoms at holding time: (b1)

t h o l d = 0

, (b2)

t h o l d = T B / 4 = 99

μs, (b3)

t h o l d = T B / 2 = 198

μs.

Fig.4 Fitting of the BO signal. Extraction of the quasimomentum distribution,

f (q)

, from the raw data (black dots) by fitting with a Lorentzian profile (blue solid line) at

t h o l d = 30 T B

. The BO signal (light-blue solid line) is obtained by subtracting the fitted offset. The center of the signal,

q = 0

, corresponds to a momentum amount of

2 n ? k

after

n

occurrences of BO, and the central peak

f c

is denoted by a black arrow. The momentum broadening,

δ q

, is extracted from the signal’s full width at half maximum (FWHM).

Fig.5 Measurement of the longitudinal coherence length. (a) The longitudinal coherence length,

l / /

, for various initial temperatures, remains largely constant across increasing holding times,

t h o l d

, for atoms at 50 nK (green squares) and 500 nK (orange diamonds). The error bar represents the standard deviation of three repeated measurements. (b) The mean longitudinal coherence length,

l ˉ / /

, depicted as a function of initial temperature, shows data for atoms below (purple circles) and above (magenta triangles) the critical temperature

T c

, averaged across various

t h o l d

periods. Error bars indicate the corresponding standard deviations.

Fig.6 Evaluation of BO lifetime. Lifetime values are derived from the central peak,

f c

, of the quasimomentum distribution for various holding times,

t h o l d

. Data points for atoms at 50 nK (purple circles) are normalized to the value at

t h o l d = 0

. Error bars denote the standard deviation from three independent measurements. The calculated lifetime,

τ

, is indicated by the point where a black dashed line at

exp ? (? 1)

intersects the solid purple fitting curve.

Fig.7 Lifetimes of BO at varying initial temperatures. (a) Lifetimes of BO across different temperatures for atoms below (purple circles) and above (magenta triangles) the critical temperature,

T c

, with an upward trend highlighted by a black dashed guideline. Error bars correspond to fitting uncertainties. (b) Scaled lifetimes of BO, normalized by the initial average density

ρ ˉ

(illustrated in the inset), exhibit two distinct

T ? 1

scaling behaviors for conditions within and outside the BEC regime, depicted by purple (

T < T c

) and magenta (

T > T c

) dashed lines, respectively. Error bars are calculated by combining fitting uncertainties in

τ

with the standard deviation of

ρ ˉ

from three measurements.

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