Using crossed electric and magnetic fields to manipulate collisions of molecules
Roman Krems University of British Columbia
UBC group:
Zhiying Li Erik Abrahamsson Timur Tscherbul
Collaborations:
Alexei Buchachenko - Moscow Grzegorz Chalasinski - Warsaw Alex Dalgarno - Harvard John Doyle - Harvard Gerrit Groenenboom - Nijmegen Sture Nordholm - Sweden Maria Szczesniak - Michigan
��������� ��� � �"��������� ���������� !�" ���#�#��
����������� �������������������
✈ v��Wrutzy t���r6����� �8����o� j~ruo!�n� ��y�k j~������o�
✈ " �w{@ou� �Zv3x!y �uo�{@� �zy k j~�8����o (O����v���� ��v x$#
✈ �O� �Ev (�t���j�� k v j~�)y t���rux � �8���Ek-j�ys� ��y�k j~������o�y�v�(&%Iv�k j�y �Ek v�x'#
✈is� � y � � k v j�y v3� �zy�k jl������o (�����v��8� ��v�x'#
✈� �~r�y�k���� ��t�r� (O����v���� ��jlkVo�{Erhj�(�t��8x �stzy �:v�(�y�v8k rhj����hv���oux
✈ � � ( ( jlkn{ jlruoq���~ru� ���ux�t���rux
��� ������
��������� ��� ������������� ���������� !�" ���#�#��
� �Ev (Ov j~rut�r� '� ��� �8����o�
��� ������
��������� ��� � �"��������� ���������� !�" ���#�#��
� �Ev (Ov j~rut�r� '� ��� �8����o�
� k �)y t�� �st�r�y�v8k��� � ��� ����� �~k � �� ���
��� ������
��������� ��� � �"��������� ���������� !�" ���#�#��
� �Ev (Ov j~rut�r� '� ��� �8����o�
� k �)y t�� �st�r�y�v8k��� � ��� ����� �~k � �� ���
� ����o t�rwy v8k�x!y v � ��jlk (Ov out�� (� � � �
��� ������
� ����� � ��� ����#�� ������� ���������� !�" ���#�#��
� �Ev (Ov j~rut�r� '� ��� �8����o�
� k �)y t�� �st�r�y�v8k��� � ��� ����� �~k � �� ���
� ����o t�rwy v8k�x!y v � ��jlk (Ov out�� (� � � �
i-v���t�� ( oEk�� %���v y x��� ��� � � � ��� �� �
��� ������
� ����� � ��� ������� ������� ���������� !�" ���#�#��
� ����� ���� � � �� ���$������� ��� ����� � ���
Centrifugal barrier
� ����o � v � � � � � � � � %Wjlkny t j����+j mwv]x ��j�y y�v�k�t�r� ��� ��� � � � �
p���y�k j~������o � t�r� ��v %Wjlkny t j��&�+j mwv x���j�y y�v�k�t�r� ��� ��� �������~� � �
��� ������
� ����� � ��� �����"� ������� ���������� !�" ���#�#��
�����&���� ��� � � �� ���$������� ��� ��� ��� �����
��� ������
� ����� � ��� ��� ��� ������� ���������� !�" ���#�#��
�����&���� ��� � � �� ���$������� ��� ��� ��� �����
�-v�� %��hjlx v�x+� � (�j�y y v8k� ����v��8� � jlk���� ���� � � � % ��� jlk x % v���t�v x
��� ������
� ����� � ��� ��� ��� ������� ���������� !�" ���#�#��
�����&���� ��� � � �� ���$������� ��� ��� ��� ������ ������������� ���� ��������Q� �� ��� ��������������� ��� � � � ��w��� ����������E����� ���������� � ��� �!� � "� ����#�%$��&� �(' � ��� ��) �+* �� ����� �
, �hj~rwy � ( �8��(&%h��y j�y t���r �st�y ��8����o:y�k j�%�% v�o (�����v �8� ��v�x
��� ������
� ����� � ��� �����"� ������� ���������� !�" ���#�#��
�����&���� ��� � � �� ���$������� ��� ��� ��� ������ ������������� ���� ��������Q� �� ��� ��������������� ��� � � � ��w��� ����������E����� ���������� � ��� �!� � "� ����#�%$��&� �(' � ��� ��) �+* �� ����� �� �����^��� � � � � ���n������� � � � � �"�� � ��� �� ����� �� � � �� ��� ������)� � ���������� � � �&� �() �+* �� ����� �
���� �� ����������������� v�x!ys� � ���uruohj�(Ov�r�y j��Ix!{�( ( v8y�k�t�v�x� v jlk�� � ���~kZy t�(OvKmljlk�t�j�y t���r:� ����uruohj�(Ov�rwy�j�� ���~ruxny j~rwy x
��� ������
� ����� � ��� ��� ��� ������� ���������� !�" ���#�#��
�����&���� ��� � � �� ���$������� ��� ��� ��� ������ ������������� ���� ��������Q� �� ��� ��������������� ��� � � � ��w��� ����������E����� ���������� � ��� �!� � "� ����#�%$��&� �(' � ��� ��) �+* �� ����� �� �����^��� � � � � ���n������� � � � � �"�� � ��� �� ����� �� � � �� ��� ������)� � ���������� � � �&� �() �+* �� ����� �
��������� �8��rux!y�jlr�y$# ���z� ��� � ��� ��� � ��^�����8� * � � ��"����� ���"� � � � ��"� � �"��"������� � � ���
� ��� � � � �^����� � � � �z� ���^�����)� � �������� ����(' � �^��� ��� ����� � ��� ��� � ����� �
� �Ev (�t�x!y�kn{ t�r y �Ev����hj~rwy � ( k v wt�(Ov�M��xnv���v�r �hj~ru� v o6� �Ev�(Ot�x!y�k {� ��rwy�k���� ��v o (�����v �8� � j�kZo�{�rhj�(�t���x
��� ������
� ����� � ��� ��� � � ������� ���������� !�" ���#�#��
�����&���� ��� � � �� ���$������� ��� ��� ��� ������ ������������� ���� ��������Q� �� ��� ��������������� ��� � � � ��w��� ����������E����� ���������� � ��� �!� � "� ����#�%$��&� �(' � ��� ��) �+* �� ����� �� �����^��� � � � � ���n������� � � � � �"�� � ��� �� ����� �� � � �� ��� ������)� � ���������� � � �&� �() �+* �� ����� �
��������� �8��rux!y�jlr�y$# ���z� ��� � ��� ��� � ��^�����8� * � � ��"����� ���"� � � � ��"� � �"��"������� � � ���
� ��� � � � �^����� � � � �z� ���^�����)� � �������� ����(' � �^��� ��� ����� � ��� ��� � ����� �
� �Ev (�t�x!y�kn{ t�r y �Ev����hj~rwy � ( k v wt�(Ov�M��xnv���v�r �hj~ru� v o6� �Ev�(Ot�x!y�k {� ��rwy�k���� ��v o (�����v �8� � j�kZo�{�rhj�(�t���x������� ��� "����������� �%� � ��� ��� �n��� � � �()������^��"� � �%� � ��� ��� ��) �+* �� ����� �
��� ������
� ����� � ��� ��� ��� ������� ���������� !�" ���#�#��
� ��� ������ �� ����������������������������� �!�"�#%$ &�'�(�) *�+, $.- / 0�-213#4$3'�1�-&35
687:9<;>=@?
� ����� � ��� ������� ������� ���������� !�" ���#�#��
� ����� ����� � �� ��� �� ��� ��� � ��� ��� ���� ���'�
� � � ��� � � � �
10-6
10-4
10-2
100
102
Temperature (K)
Typ
ical
Rat
e C
oeff
icie
nt room temperature
��� ���������������������� "!�#%$'&)(�*,+-#�.0/,/21436587,7,*09
��� ������
� ����� � ��� � ��#�� ������� ���������� !�" ���#�#��
� ����� ����� � �� ��� �� ��� ��� � ��� ��� ���� ���'�
� � � ��� � � � �
10-6
10-4
10-2
100
102
Temperature (K)
Typ
ical
Rat
e C
oeff
icie
nt room temperature
��� ���������������������� "!�#%$'&)(�*,+-#�.0/,/21436587,7,*09
��� ������
� ����� � ��� � �n��� ������� ���������� !�" ���#�#��
� ����� ����� � �� ��� �� ��� ��� � ��� ��� ���� ���'�
� � � ��� � � � �
10-6
10-4
10-2
100
102
Temperature (K)
Typ
ical
Rat
e C
oeff
icie
nt room temperature
��� ���������������������� "!�#%$'&)(�*,+-#�.0/,/21436587,7,*09
��� ������
� ����� � ��� � ���"� ������� ���������� !�" ���#�#��
� ����� ����� � �� ��� �� ��� ��� � ��� ��� ���� ���'�
� � � ��� � � � �
10-6
10-4
10-2
100
102
Temperature (K)
Typ
ical
Rat
e C
oeff
icie
nt room temperature
��� ���������������������� "!�#%$'&)(�*,+-#�.0/,/21436587,7,*09
��� ������
� ����� � ��� � � ��� ������� ���������� !�" ���#�#��
� ����� ����� � �� ��� �� ��� ��� � ��� ��� ���� ���'�
10-6
10-4
10-2
100
102
Collision energy (Kelvin)
Typ
ical
cro
ss s
ectio
n
��� ������
� ����� � ��� � � ��� ������� ���������� !�" ���#�#��
� ����� ����� � �� ��� �� ��� ��� � ��� ��� ���� ���'�
10-6
10-4
10-2
100
102
Collision energy (Kelvin)
Typ
ical
cro
ss s
ectio
n
Wigner’s laws:elastic cross section ~ constantreaction cross section ~ 1/velocity
��� ������
� ����� � ��� � ���"� ������� ���������� !�" ���#�#��
� ����� ����� � �� ��� �� ��� ��� � ��� ��� ���� ���'�
Wigner’s laws:elastic cross section ~ constantreaction cross section ~ 1/velocity
rate ~ velocity cross sectionelastic rate ~ 0reaction rate ~ constant
x
��� ������
� ����� � ��� � � ��� ������� ���������� !�" ���#�#��
� ����� ����� � �� ��� �� ��� ��� � ��� ��� ���� ���'�
� � � �� � � �������� ��������� � � �������3���~��#����� � �� ��� �
��� ����� � ��� � ��������� � � � � � � �� � � � �"�"��� ��� � �"� � � �"����'��#�� � � � �� ��� �
��� ������
� ����� � ��� � � � � ������� ���������� !�" ���#�#��
� ��� � ��2��� ����������� ������� � �2�����#%$ &�'���� - *�� � $.-/ 0�-21�#%$�'�1�-&��
687:9<;>=@?
� ����� � ��� � � ��� ������� ���������� !�" ���#�#��
� ��� � ��2��� ����������� ������� � �2�����#%$ &�'���� - *�� � $.-/ 0�-21�#%$�'�1�-&��� )�-�� / #�� ��- -21�� -�� (�� - � $ �
687:9<;>=@?
� ����� � ��� � ����� ������� ���������� !�" ���#�#��
� ��� � � � ���� � ��� �� ��������� � ��� � � � � ��� �
��� ������
� ����� � ��� � ��#�� ������� ���������� !�" ���#�#��
� ��� � � � ���� � ��� �� ��������� � ��� � � � � ��� �
v=0, j=0
3Σ
3Π
$ �������0�������� � �� ����������� � ���������� ������ ����������������! �"�#$�&%('�������"*)+'�,��-��.&�/"102�-'�354-�-3�"�%6��783�.�9;:��;�-�-9��<7-"�=�=�=+>?�@ ���BA��� ���C@ �C�,������5@ ��D(@5@�E�GF�'�3�"�H/�I�8�J�!KJ���C"�LM'��-NO��3�"�P+.CKJ35�-���G"�02�-'�354-�-3�"�=�=�=�>Q � ����R��@��5@ ��@ � ������,�S��T�U�,��@5���%����6AV@ �� ���%(�-' W��IK&"1)��XKJYZ�IK&"�[��I�J�IKJ7-"�\5KJ'��&];KJ'�^`_�"�=�=�=+>Q ��� �a� ����b�GcVd5K`�C_��CN6"��;_���ef�IK8:�g2�- �"1=�=�=+>?���@5@h@;ijE���%�����,���k295l5�`�;"�\5KJ'��&]mKJ'�^`_�"502�!KJ78_;d��C^`_�"1=�=�=�>�(�jn2@ �ob,�� ���0�������b�p#$.& ;����"�[��I�J�IKJ7-"�=�=�=+>q E+����� 2�$�%��EV�,� @rJ�,���5@ �����sD � ��b�p#$�&%('�������"�=�=�=�>tu@5� ����%� � �� �����sD ����b��k295l5�`�;"502�!KJ78_;d��C^`_�"1=�=�=�>Q�v �UE������@5�����h�����,��� ��bwA v �5�,��� ����� �,�%�xD � � �y�%��� � ����,� � ��Z��� ���%(�-' W��IK&"�=�=�=�>�� ��� � ��C�jz&A�2����z � �"��@{�5�,��� ����� �,�%�x�Z� �C����Eu�U�,� @�������@ ���P+_��C3*];���IK&"�=�=�=�>
��� ������
� ����� � ��� � � � � ������� ���������� !�" ���#�#��
Controlled chemistry
controlExternal field
(Shapiro, ...)Coherent control
Controlled dynamics
��� ������
Principles of external �eld control of molecular dynamics
• Close or open channels by the Zeeman/Stark e�ect
• Break the spherical symmetry of the problem
• Mitigate the role of centrifugal barriers in the reaction
• Induce Feshbach resonances that enhance reactivity
• Suppress or enhance the role of spin-orbit interactions
• Induce anisotropic interactions
� ����� � ��� � � ��� ������� ���������� !�" ���#�#��
� � � ���� ��� ����� ������� ��� ��� ��������� ��� ���� ��
m
mmm
No fieldHigh field
��� ������
� ����� � ��� � � ��� ������� ���������� !�" ���#�#��
� � � ���� ��� ����� ������� ��� ��� ��������� ��� ���� ��
i-v � � � � � � �8��(&%���v (
-1 -0.75 -0.5 -0.25 0-1
0
1
2
Eig
enph
ase
sum
(σ/
π)
-0.5 -0.4 -0.3 -0.2 -0.1 0
0
0.5 B = 0.1 Tesla
��� ������
� ����� � ��� � ���"� ������� ���������� !�" ���#�#��
� � � ���� ��� ����� ������� ��� ��� ��������� ��� ���� ��
i-v � � � � � � �8��(&%���v (
-1 -0.75 -0.5 -0.25 0-1
0
1
2
Eig
enph
ase
sum
(σ/
π)
-0.5 -0.4 -0.3 -0.2 -0.1 00
1
2
-0.5 -0.4 -0.3 -0.2 -0.1 0
0
0.5 B = 0.1 Tesla
B = 0.3 Tesla
��� ������
� ����� � ��� � � ��� ������� ���������� !�" ���#�#��
� � � ���� ��� ����� ������� ��� ��� ��������� ��� ���� ��
i-v � � � � � � �8��(&%���v (
Energy (cm-1
)
-1 -0.75 -0.5 -0.25 0-1
0
1
2
Eig
enph
ase
sum
(σ/
π)
-0.5 -0.4 -0.3 -0.2 -0.1 00
1
2
-0.5 -0.4 -0.3 -0.2 -0.1 0
0
0.5 B = 0.1 Tesla
B = 0.3 Tesla
B = 1 T
��� ������
� ����� � ��� � � � � ������� ���������� !�" ���#�#��
� � � ���� ��� ����� ������� ��� ��� ��������� ��� ���� ��
i-v � � � � � � �8��(&%���v (
Energy (cm-1
)
-5 -4 -3 -2 -1 0
0
2
4
-1 -0.75 -0.5 -0.25 0-1
0
1
2
Eig
enph
ase
sum
(σ/
π)
-0.5 -0.4 -0.3 -0.2 -0.1 00
1
2
-0.5 -0.4 -0.3 -0.2 -0.1 0
0
0.5 B = 0.1 Tesla
B = 0.3 Tesla
B = 1 T
B = 2 Tesla
��� ������
� ����� � ��� � � ��� ������� ���������� !�" ���#�#��
� � � ���� ��� ����� ������� ��� ��� ��������� ��� ���� ��
i-v � � � � � � �8��(&%���v (
-6 -5 -4 -3 -2 -1 0
Energy (cm-1
)
0
2
4
-5 -4 -3 -2 -1 0
0
2
4
-1 -0.75 -0.5 -0.25 0-1
0
1
2
Eig
enph
ase
sum
(σ/
π)
-0.5 -0.4 -0.3 -0.2 -0.1 00
1
2
-0.5 -0.4 -0.3 -0.2 -0.1 0
0
0.5 B = 0.1 Tesla
B = 0.3 Tesla
B = 1 T
B = 2 Tesla
B = 3 Tesla
��� ������
� ����� � ��� � ����� ������� ���������� !�" ���#�#��
� � � ���� ��� ����� ������� ��� ��� ��������� ��� ���� ��
0 0.5 1 1.5 2 2.5 3
Magnetic field (Tesla)
10-11
10-10
10-9
Lif
etim
e of
the
com
plex
(se
c)
��� ������
� ����� � ��� ���"#�� ������� ���������� !�" ���#�#��
� ��� ��� ���� � � � ���'� �$��� � � � � � �� �
� j�k � ��rqj�y ��( t�rqj ( j� wrEv y t�� �hv���o
0.4 0.6 0.8 1B, Tesla
0
10
20
30
40
Ene
rgy
(cm
-1)
3P0
3P1
3P
2
mj=+1
mj=0
��� ������
� ����� � ��� ���!��� ������� ���������� !�" ���#�#��
� ��� ��� ���� � � � ���'� �$��� � � � � � �� �
� � � � � �Vi-v ��������t�x�t���rux j�y � v8k�� (�j� wrEv y t�� �hv ��o
10-5
10-4
10-3
10-2
10-1
100
T (K)
10-16
10-14
10-12
10-10
Rat
e co
nsta
nt (
cm3 s-1
) elastic
3 P 13 P 0
� �C@�� �o@;�)����"#�$ & � ����#�+,.,+���+0/%3 & 9 3 /�+,+0/�9
��� ������
� ����� � ��� �����"� ������� ���������� !�" ���#�#��
� ��� ��� ���� � � � ���'� �$��� � � � � � �� �� �lk �ht�ouoEv r � � # � � � � y�k j~rux t�y t���r � � � � ! j~�ux x
10-9
10-6
10-3
100
Collision energy (K)
10-4
10-3
10-2
10-1
100
101
102
103
Cro
ss s
ectio
n (Å
2 )
� �C@�� � 2��� � ���b02�����%#�$ &����,*�#%+�58.�10+�� 3 /�+,+�.09
��� ������
� ����� � ��� ��� ��� ������� ���������� !�" ���#�#��
� ��� ��� ���� � � � ���'� �$��� � � � � � �� �� �lk �ht�ouoEv r � � # � � � � y�k j~rux t�y t���r � � � � ! j~�ux x
10-9
10-6
10-3
100
Collision energy (K)
10-4
10-3
10-2
10-1
100
101
102
103
Cro
ss s
ectio
n (Å
2 )
� �C@�� � 2��� � ���b02�����%#�$ &����,*�#%+�58.�10+�� 3 /�+,+�.09
��� ������
� ����� � ��� ��� ��� ������� ���������� !�" ���#�#��
� ��� ��� ���� � � � ���'� �$��� � � � � � �� �� �lk �ht�ouoEv r � � # � � � � y�k j~rux t�y t���r � � � � � ! j~�ux x
10-9
10-6
10-3
100
Collision energy (K)
10-4
10-3
10-2
10-1
100
101
102
103
Cro
ss s
ectio
n (Å
2 )
� �C@�� � 2��� � ���b02�����%#�$ &����,*�#%+�58.�10+�� 3 /�+,+�.09
��� ������
� ����� � ��� �����"� ������� ���������� !�" ���#�#��
� ��� ��� ���� � � � ���'� �$��� � � � � � �� �� �lk �ht�ouoEv r � � # � � � � y�k j~rux t�y t���r � � � � ����� ! j~�ux x
10-9
10-6
10-3
100
Collision energy (K)
10-4
10-3
10-2
10-1
100
101
102
103
Cro
ss s
ectio
n (Å
2 )
� �C@�� � 2��� � ���b02�����%#�$ &����,*�#%+�58.�10+�� 3 /�+,+�.09
��� ������
� ����� � ��� ��� ��� ������� ���������� !�" ���#�#��
� ��� ��� ���� � � � ���'� �$��� � � � � � �� �� �lk �ht�ouoEv r � � # � � � � y�k j~rux t�y t���r � � � � �����~� ! j~�ux x
10-9
10-6
10-3
100
Collision energy (K)
10-4
10-3
10-2
10-1
100
101
102
103
Cro
ss s
ectio
n (Å
2 )
� �C@�� � 2��� � ���b02�����%#�$ &����,*�#%+�58.�10+�� 3 /�+,+�.09
��� ������
� ����� � ��� ��� � � ������� ���������� !�" ���#�#��
� ��� ��� ���� � � � ���'� �$��� � � � � � �� �� �~k �ht�ouoEv r6v ��v��)y k���rut��sy�k j~rux t�y t��~r@j�y � v8k�� y�v (&% v8k j�y �Ek�v
0 10000 20000 30000 40000
Magnetic field (Gauss)
10-20
10-16
10-12
Rat
e co
nsta
nt (
cm3 se
c-1)
� �C@�� � 2��� � ���b02�����%#�$ &����,*�#%+�58.�10+�� 3 /�+,+�.09
��� ������
Controlling Collisions of Ultracold Atoms with dc Electric Fields
R. V. Krems*Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
(Received 14 August 2005; revised manuscript received 12 March 2006; published 28 March 2006)
It is demonstrated that elastic collisions of ultracold atoms forming a heteronuclear collision complexcan be manipulated by laboratory practicable dc electric fields. The mechanism of electric field control isbased on the interaction of the instantaneous dipole moment of the collision pair with external electricfields. It is shown that this interaction is dramatically enhanced in the presence of a p-wave shape orFeshbach scattering resonance near the collision threshold, which leads to novel electric-field-inducedFeshbach resonances.
DOI: 10.1103/PhysRevLett.96.123202 PACS numbers: 34.50.!s, 34.20.Gj
The creation of ultracold atoms and molecules has led tomany ground-breaking discoveries described in recent re-view articles [1]. Particularly interesting is the possibilityto control interactions of ultracold atoms and moleculeswith external electric and magnetic fields [2]. External fieldcontrol of atomic and molecular dynamics may lead tonovel spectroscopy methods, provide detailed informationon mechanisms of chemical reactions, and allow for thedevelopment of a scalable quantum computer [3]. Externalfields may be used to tune the scattering length for mo-lecular interactions and alleviate the evaporative cooling ofmolecules to ultracold temperatures [4]. Collisions of ul-tracold atoms can be controlled by magnetic fields usingFeshbach resonances [5] or by lasers [6,7]. Here, we showthat ultracold collisions of atoms forming a heteronuclearcollision complex can also be controlled by dc electricfields due to the interaction of the instantaneous dipole mo-ment of the collision pair with external fields. The interac-tion is dramatically enhanced in the presence of a p-wavescattering resonance near collision threshold, which allowsfor the possibility to tune the scattering length of ultracoldatoms by laboratory available electric fields. This providesa new mechanism to control elastic scattering, inelasticenergy transfer and chemical reactions in collisions ofatoms and molecules at zero absolute temperature.
Electric field control of atomic and molecular interac-tions may offer several advantages over magnetic fieldcontrol and optical methods. The evaporative cooling ofatoms and molecules is most easily achieved in a magnetictrap, where magnetic field control of collisions may becomplicated due to varying magnetic fields of the trap.Electric fields induce anisotropic interactions. The studyand control of anisotropic collision properties at ultracoldtemperatures may uncover new phenomena in condensedmatter physics—hence the recent interest in polar Bose-Einstein condensates [8]. Anisotropic interactions mayalso be used to connect qubits in a quantum computer[3], and schemes for electric field control of atomic andmolecular interactions are particularly relevant for quan-tum computation. Electric field control may be applicableto systems without magnetic moments or systems, for
which s-wave Feshbach resonances cannot be induced ina practicable interval of magnetic fields. Finally, electricfield control of atomic collisions may provide a sensitiveprobe of scattering resonances corresponding to nonzeropartial waves so the mechanism described here can be usedfor high-precision measurements of molecular states nearthe dissociation threshold.
Marinescu and You [9] proposed to control interactionsin ultracold atomic gases by polarizing atoms with strongelectric fields. The polarization changes the long-rangeform of the atom-atom interaction potential and modifiesthe scattering length. The interaction between an atom andan electric field is, however, extremely weak, and fields ofas much as 250 to 700 kV=cm were required to alter theelastic scattering cross section of ultracold atoms in thecalculation of Marinescu and You. The maximum dc elec-tric field currently available in the laboratory is about200 kV=cm [10]. We propose an alternative mechanismfor electric field control of ultracold atom interactions anddemonstrate that the scattering length of ultracold atomscan be manipulated by electric fields below 100 kV=cm.
We consider collisions in binary mixtures of ultracoldgases. Mixtures of ultracold alkali metal atoms have beencreated by several experimental groups [11,12]. When twodifferent atoms collide, they form a heteronuclear colli-sion complex which has an instantaneous dipole momentso it can interact with an external electric field. The inter-action is weak. The dipole moment function of the colli-sion complex is typically peaked around the equilib-rium distance of the diatomic molecule in the vibration-ally ground state and quickly decreases as the atoms sepa-rate. Only a small part of the scattering wave functionsamples the interatomic distances, where the dipole mo-ment function is significant. At the same time, the inter-action with an electric field couples states of differentorbital angular momenta. The zero angular momentums-wave motion of ultracold atoms is coupled to an ex-cited p-wave scattering state, in which the colliding atomsrotate about each other with the angular momentum l "1 a:u: The probability density of the p-wave scatteringwave function at small interatomic separations is very
PRL 96, 123202 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending31 MARCH 2006
0031-9007=06=96(12)=123202(4)$23.00 123202-1 2006 The American Physical Society
d
E
0 1000 2000 3000 4000 5000 6000 7000
Magnetic field (Gauss)
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Pote
ntia
l ene
rgy
(K)
The energy of Li and Cs in the states
with mfLi = 1 and m
fCs
= 1
0 1000 2000 3000 4000 5000 6000 7000
Magnetic field (Gauss)
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Pote
ntia
l ene
rgy
(K)
The energy of Li and CsTotal angular momentum projection M=2
� ������� ������"����� � ������� ,����������� !"��#%$&�('()�*+'���*�*�,
Feshbach resonance
� ��������
1460 1465 1470 1475 1480 1485 1490
Magnetic field (Gauss)
104
105
S-w
ave
elas
tic s
catte
ring
cro
ss s
ectio
n (a
.u.)
1600 1800 2000 2200
Magnetic field (Gauss)
10-3
100
103
10-3
100
103
106
Cro
ss s
ectio
n (Å
2 )
Zero electric field
10-3
100
103
1600 1800 2000 2200
Magnetic field (Gauss)
10-3
100
103
106
Cro
ss s
ectio
n (Å
2 )
Zero electric field
100 kV/cm
70 80 90 100 110
Electric Field (kV/cm)
102
104
106
108
Cro
ss s
ectio
n (Å
2 )PRL 96, 123202 (2006)
Controlling spin relaxation of molecules with electric fields
1/2j =
N = 1
0N =
j = 3/2
j = 1/2
0 25 50 75 100 125 150
Electric field (kV/cm)
3×10-6
4×10-6
5×10-6
6×10-6
7×10-6
8×10-6
Cro
ss s
ectio
n, Å
2
CaH
0 25 50 75 100 125 150
Electric field (kV/cm)
10-5
10-4
Cro
ss s
ectio
n, Å
2
CaH
CaD
0 25 50 75 100 125 150
Electric field (kV/cm)
10-5
10-4
10-3
10-2
10-1
Cro
ss s
ectio
n, Å
2
CaH
CaD
Molecule with rot constant 1 K
0
2
4
Ene
rgy,
cm
-1
0 20 40 60Electric field (kV/cm)
4
4.5
5
5.5
∆E
, cm
-1
CaD; B = 0.1 T
0
2
4
Ener
gy, cm
-1
0 20 40 60
Electric field (kV/cm)
4
4.5
5
5.5
!E
, cm
-1
CaD; B = 0.1 T
1/2j =
N = 1
0N =
j = 3/2
j = 1/2
0 20 40 60
Electric field, kV/cm
2
2.1
2.2
2.3E
nerg
y, c
m-1
CaD; B = 4.7 T
4.4 4.6 4.8 5
Magnetic field, T
10-2
100
102
Cro
ss s
ectio
n, Å
2
0 20 40 60 80
Electric field, kV/cm
10-2
100
102
Cro
ss s
ectio
n, Å
2
E = 20 kV/cmE = 20 kV/cm
Spin relaxationin CaD - He collisions
Zero electric field
� ������� ������"����� � ������� )", �������� !"��#%$&�('()�*+'���*�*�,
� � ����� � � ��� � ��� � ������� ������ �
� q � ��� ��� � q�p � ��� � � q�p � � q
triplet state
singlet state
A + BCB + AC
� ��������
Rigorous scattering calculations with �elds are very di�cult
Rigorous scattering calculations with �elds are very di�cult
No external fields
15 calculations with less than
yesyesyes 128 coupled states each
Rigorous scattering calculations with �elds are very di�cult
No external fields
15 calculations with less than
yesyesyes 128 coupled states each
In a magnetic field
31 calculations with up to
yesyesyes 808 coupled states each
Rigorous scattering calculations with �elds are very di�cult
No external fields
15 calculations with less than
yesyesyes 128 coupled states each
Parallel electric and magnetic fields
B E
31 calculations with up to
yesyesyes 808 coupled states each
Rigorous scattering calculations with �elds are very di�cult
No external fields
15 calculations with less than
yesyesyes 128 coupled states each
Parallel electric and magnetic fields
B E
31 calculations with up to
yesyesyes 808 coupled states each
Nonparallel electric and magnetic fields
BE
1 calculation with
yes 10,368 coupled di�erential equations
0 20 40 60 80
Angle between the fields, degrees0
50
100
150
200
250C
ross
sec
tion,
Ų
B = 4.7 T
Zeeman relaxation in CaD - He collisions
E = 20 kV/cm
Conclusions
Conclusions
70 80 90 100 110
Electric Field (kV/cm)
102
104
106
108
Cro
ss s
ectio
n (Å
2 )
PRL 96, 123202 (2006)
• Electric-�eld-induced resonances• May also occur in molecule - molecule collisionsy (The dipole moment of RbCs - RbCs is 6 Debye)
Conclusions
70 80 90 100 110
Electric Field (kV/cm)
102
104
106
108
Cro
ss s
ectio
n (Å
2 )
PRL 96, 123202 (2006)
• Electric-�eld-induced resonances• May also occur in molecule - molecule collisionsy (The dipole moment of RbCs - RbCs is 6 Debye)
Conclusions
70 80 90 100 110
Electric Field (kV/cm)
102
104
106
108
Cro
ss s
ectio
n (Å
2 )
PRL 96, 123202 (2006)
• Electric-�eld-induced resonances• May also occur in molecule - molecule collisionsy (The dipole moment of RbCs - RbCs is 6 Debye)
Conclusions
70 80 90 100 110
Electric Field (kV/cm)
102
104
106
108
Cro
ss s
ectio
n (Å
2 )
PRL 96, 123202 (2006)
• Electric-�eld-induced resonances• May also occur in molecule - molecule collisionsy (The dipole moment of RbCs - RbCs is 6 Debye)
Conclusions
70 80 90 100 110
Electric Field (kV/cm)
102
104
106
108
Cro
ss s
ectio
n (Å
2 )
PRL 96, 123202 (2006)
• Electric-�eld-induced resonances• May also occur in molecule - molecule collisionsy (The dipole moment of RbCs - RbCs is 6 Debye)
0 25 50 75 100 125 150
Electric field (kV/cm)
10-5
10-4
10-3
10-2
10-1
Cro
ss s
ectio
n, Å
2
CaH
CaD
Molecule with rot constant 1 K
Conclusions
70 80 90 100 110
Electric Field (kV/cm)
102
104
106
108
Cro
ss s
ectio
n (Å
2 )
PRL 96, 123202 (2006)
• Electric-�eld-induced resonances• May also occur in molecule - molecule collisionsy (The dipole moment of RbCs - RbCs is 6 Debye)
0 25 50 75 100 125 150
Electric field (kV/cm)
10-5
10-4
10-3
10-2
10-1
Cro
ss s
ectio
n, Å
2
CaH
CaD
Molecule with rot constant 1 K
4.4 4.6 4.8 5 5.2Magnetic field, T
10-2
100
102
Cro
ss s
ectio
n, Å
2
Zero electric fieldE = 20 kV/cmE = 40 kV/cm
0 20 40 60 80
Electric field, kV/cm
10-2
100
102
Cro
ss s
ectio
n, Å
2
20 kV/cm 40 kV/cm
Zero electric field
Conclusions
70 80 90 100 110
Electric Field (kV/cm)
102
104
106
108
Cro
ss s
ectio
n (Å
2 )
PRL 96, 123202 (2006)
• Electric-�eld-induced resonances• May also occur in molecule - molecule collisionsy (The dipole moment of RbCs - RbCs is 6 Debye)
0 25 50 75 100 125 150
Electric field (kV/cm)
10-5
10-4
10-3
10-2
10-1
Cro
ss s
ectio
n, Å
2
CaH
CaD
Molecule with rot constant 1 K
4.4 4.6 4.8 5 5.2Magnetic field, T
10-2
100
102
Cro
ss s
ectio
n, Å
2
Zero electric fieldE = 20 kV/cmE = 40 kV/cm
0 20 40 60 80
Electric field, kV/cm
10-2
100
102
Cro
ss s
ectio
n, Å
2
20 kV/cm 40 kV/cm
Zero electric field
0 20 40 60 80
Angle between the fields, degrees0
50
100
150
200
250
Cro
ss s
ectio
n, Å
²
B = 4.7 T
Zeeman relaxation in CaD - He collisions
E = 20 kV/cm
Review papers:
some-space Eur. Phys. J. D 31, 149 (2004).
some-space Int. Rev. Phys. Chem. 24, 99 (2005).
Quantum Chemistry and Ultracold Physics
• Interactions between atoms and molecules at long range
some-space Interaction Anisotropy
some-space Spectroscopic accuracy
some-space Heavy (Metallic) Systems
• E�ects of �elds on molecular structure
• Dipole moment functions for complexes of atoms and molecules
• Non-adiabatic e�ects
Review papers:
some-space Eur. Phys. J. D 31, 149 (2004).
some-space Int. Rev. Phys. Chem. 24, 99 (2005).